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1665:) I chose a position that makes sense in respect to the usual orientation of the coordinate axes. I think it is better to show this compound in a way where one of the cubes has the "usual" orientation. And I think it makes sense to choose a "special" color for that cube. If you feel like creating a Stella image with less random orientation and colors, I would not mind if you replace my file. But in any case, there should be a link to an animation if there is one (unless the animation is prohibitively terrible, which I think is not the case here).
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38:, you wrote a definition in a separate section of the graph connectivity article, in order to provide an adequate anchor for a redirect. This is well done, I think; but you (incidently, or after careful consideration?) also included examples, which include make the empty graph among the connected ones. (The graph with no vertex also has no edge.) This, I find unusual, and not so good.
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1691:(Are you trying to demonstrate that the wikipedia metalanguage is Turing complete?) Thus, and since you clearly make use of them for purposes you have thought out, I do consider these templates as 'de facto yours', even if technically you have declined all rights to any pages outside your own user page and any subpage thereof.
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Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum
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So, for these and similar reasons, when I allow the empty graph, I consider it as "not connected". In this way, a tree is demanded to be non-empty, while I allow the empty forest - a forest in my opinion is best defined as any acyclic graph, i. e., as the disjoint union of zero or more trees (whence
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Another example: A connected component of a graph often is defined as a maximal connected subgraph. Thus, with your definitions, the empty graph should have one connected component, namely itself. As a consequence, the theorem, that the number of components in a disjoint union of graphs equals the
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I see that you are making some fairly 'mathematical' templates (which yield 'mathematical effects' rather than e. g. list some kind of mathematical concepts). I find them quite interesting. They are written in a style of their own - or, I should say, a personal style of yours, with unusual effects.
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Hi. Having the same image style across different articles is nice, but that does not mean that a Stella image should automatically be preferred. One in a different style can still be the better image for that particular solid. (In tables where the images are shown next to each other, I would give a
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Thanks very much for your quackage to me back in
November 2016. I regret that I missed it until Knowledge recently notified me. It appears that you, like me, have been troubled by the many unstated assumptions underlying practically every discussion of permutations and the process of permutation. I
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I therefore would like to remove your zero vertex example. However, if you added it on purpose, and especially if you have references where the empty graph both is allowed and considered to be connected, then we could retain it, but with the warning that only some authors considers the empty graph
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Maybe someday the many disciplines that make use of permutations could employ your framework as a guide, announce in advance what kind of notation is to be used in a paper or presentation, and thereby restore some peace of mind to those of us who become confused and uncomfortable when concepts and
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1706:. (Our meta language largely is a markup language, where often we expect an end-of-something to follow any beginning-of-something we insert.) The categories of course are inserted within the noinclude part, and thus only should make your templates accessible also for others. In fact, we expect
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I find this discussion quite interesting, and I would like to respond to your question about sources that use a certain type of notation, but I do not understand your subscripts. Could you please explain the subscripts and/or describe in more detail what you are referring to? Thanks
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infobox to clash with the Stella images that are used in pretty much almost every other uniform polyhedron article. I replaced it because of that, before you undid it. I have no intention of causing a dumb edit war, so feel free to take my advice or ignore it as you see fitting. –
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1826:. The point of these templates is just to keep the source of the articles tidy. I don't remember that I ever created a complicated template on Knowledge. (There are some on Commons and Wikiversity.) I don't like the template language, so this is not likely to change.
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Here is an example: A tree commonly is defined as a connected acyclic graph. It also is said to have the property (order = size+1). However, with your definitions, the empty graph would be both connected and acyclic; but with both order and size equal to zero.
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Now, many authors tacitly or explicitly demand that graphs be non-empty; i. e., they do not allow an empty graph. (If my memory is correct, e. g. Diestl demands this explicitly.) Now, personnally, I prefer to consider also the empty graph
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I plan to make a re-alphabetisation of the categorisation of some permutation template I saw, too (sorting in the first place by the Greek letter Τ rather than by the template name). Again, if you dislike it, just revert!
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mandatory, since many templates are employed in manners not directly related to additions to articles. I hope and believe that these changes should not be to any problem for you; otherwise I would not have made them.
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Ay Ex". What is perhaps more interesting is that (if my poking around your data tables linked from OEIS is accurate), these already capture all edges for the 3-variable version: they are all of the form "Ax ... -:
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consider the empty graph as connected. If I did, I would either have to make a numerous amount of exceptions in other definitions and calculations, or run into rather weird changes of how graphs behave.
2192:. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose
2058:. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose
1968:. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose
1880:. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose
1575:. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose
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To me L/R is only a superficial difference, corresponding to flipping a matrix multiplication along the main diagonal. A/P is about a different matrix multiplication, no matter how it is flipped.
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Thanks for your reply. I don't intend to publish my stuff in a more classical format. I am way too addicted to nested collapsible boxes, and I would rather have more interactivity than less.
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Hi
Joergen, I don't do much work in Knowledge, and I have no opinion on the categorization of templates. Thanks for fixing it. A template that is indeed in my personal style is
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1718:= 3). I also added what I thought was a suitable category for any user who might have direct use for your template in article editing. (Such a categorisation of a template is
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sums of the component numbers of these graphs, would have be to be modified, by subtracting the number of components who are empty graphs, but adding one, if they all are.
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What do you think about the terminology I use in the article (active/passive)? It makes sense to me, and I think it helps to understand the problem and the article.
101:(Another, rather minor point: The rest of that article uses the term "vertex" instead of "node". This should be easy and uncontroversial to fix, though, I think.)
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article without sources. The simple reason is, that no one seems to use what I call passive permutations. Therefore I had the following statement in the article:
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I just saw that you've been around for a dozen more years than I thought. Thus, I guess I unnecessarily explained things a bit too much in deatail. Excuse me!
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am very glad you have written what appears to be an excellent article on the topic. Have you published that piece, or a variant, in some journal or on ArXiv?
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stronger preference to consistency.) What I dislike about most of these Stella images is the random orientation of the solid. In my polyhedron images (e.g.
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Nevertheless, we do prefer some organisation of the very large number of pages in the project. I therefore boldly add two categories to your
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It seems that in your terminology this difference is somehow about left vs. right, rather than active vs. passive - which I don't understand.
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Numbers of edges don't seem to be prominent in the OEIS. I was also surprised that no sequence counts the edges in weak order diagrams like
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I don't really understand what you are trying to say. But it sounds like the answer should already be in the data on GitHub for
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did not already exist, but I suppose the number of edges in these Hasse diagrams is long known, hidden is some dusty books.
963:{\displaystyle \sigma .(x_{1},x_{2},\ldots ,x_{n})=(x_{\sigma ^{-1}(1)},x_{\sigma ^{-1}(2)},\ldots ,x_{\sigma ^{-1}(n)})~~~}
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The active interpretation of a permutation should usually be seen as correct, and the passive one as a misunderstanding.
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Hi. To me it was only important to add a section with a clear definition. Feel free to modify the details as you like.
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As you can see {{Lorem ipsum|2}} gives me two paragraphs of Latin gibberish, but only on
Knowledge.-- .... Back to
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For A/P compare box 12 and box 16 in my article. For L/R compare left and right matrix multiplication in each box.
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1120:{\displaystyle ~~~(x_{1},x_{2},\ldots ,x_{n}).\sigma =(x_{\sigma (1)},x_{\sigma (2)},\ldots ,x_{\sigma (n)})\,}
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Looking at that today, I think the whole left/right thing is something irrelevant which I should have omitted.
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as a (simple) graph, since this on some points makes the graph theory smoother. However, then, I do
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There is also the connectivity and connectedness connection, which breaks down for the empty graph.
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Ex. The edges of the 2-variable Hasse diagram are all of the following form: "Ax ... -: -->
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This might be not very important, but I find the style of the animation on the
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Maybe one day we will see a decent forum format for
Wikimedia discussion pages.
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is likely misguided and should probably be reverted. I have explained why at
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I did not write those lines! That is part of someone's reply to what I wrote.
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describes the
Committee's roles and responsibilities in greater detail.
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describes the
Committee's roles and responsibilities in greater detail.
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describes the
Committee's roles and responsibilities in greater detail.
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describes the
Committee's roles and responsibilities in greater detail.
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describes the
Committee's roles and responsibilities in greater detail.
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it also is characterised by the equation "order = size+#(components)").
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are allowed to vote. Users with alternate accounts may only vote once.
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are allowed to vote. Users with alternate accounts may only vote once.
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are allowed to vote. Users with alternate accounts may only vote once.
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are allowed to vote. Users with alternate accounts may only vote once.
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If I'm wrong, or you for any other reason dislike my edit, please just
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are allowed to vote. Users with alternate accounts may only vote once.
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Knowledge:Redirects for discussion/Log/2024 January 20 § COM:OVERWRITE
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Template:2-ary truth table; disjunction with implication and negation
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Template:2-ary truth table; disjunction with implication and negation
2274:. Anyone, including you, is welcome to comment on this redirect at
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But it's not a terminology I have found anywhere else - except in
2217:. If you no longer wish to receive these messages, you may add
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If you wish to participate in the 2023 election, please review
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If you wish to participate in the 2019 election, please review
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is now open until 23:59 (UTC) on Monday, 7 December 2020. All
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notation are used inconsistently from one moment to the next.
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https://en.wikiversity.org/Inversion_(discrete_mathematics)
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684:{\displaystyle (x_{\pi ^{-1}(1)},\dots ,x_{\pi ^{-1}(n)})}
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Hi, I think your addition of
Jamnitzer to the article on
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Template:2-ary truth table; disjunction with implication
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Template:2-ary truth table; disjunction with implication
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is now open until 23:59 on Monday, 2 December 2019. All
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is the panel of editors responsible for conducting the
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is the panel of editors responsible for conducting the
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is the panel of editors responsible for conducting the
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is the panel of editors responsible for conducting the
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is the panel of editors responsible for conducting the
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to determine whether its use and function meets the
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2434:. You are invited to comment on the discussion at
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357:{\displaystyle (x_{\pi (1)},\dots ,x_{\pi (n)})}
1710:templates to be found in some (sub)category of
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1476:I have sent you a note about a page you started
765:Now I see what you mean. Thanks for explaining.
364:? I would be happy to include them. Greetings,
2437:the entry on the Templates for discussion page
2397:the entry on the Templates for discussion page
2357:the entry on the Templates for discussion page
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1365:Ex ..." (with the same "...") or "Ex Ay -: -->
1802:. But I think there is nothing unusual about
1171:OMG! That is a very confusing way to answer.
410:I don't understand what you don't understand.
8:
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781:Talk:Permutation#Major_Problem_with_Notation
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287:{\displaystyle (x_{1},\dots ,x_{n})}
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1704:. I also add a </noinclude: -->
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196:(And I guess it harmonizes with
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2280:until a consensus is reached.
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68:
2186:Arbitration Committee
2169:Hello! Voting in the
2125:The Original Barnstar
2052:Arbitration Committee
2035:Hello! Voting in the
1962:Arbitration Committee
1946:Hello! Voting in the
1874:Arbitration Committee
1858:Hello! Voting in the
1569:Arbitration Committee
1553:Hello! Voting in the
1492:page curation process
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1793:3-el perm inversions
1783:4-el perm inversions
1488:User:Bishal Shrestha
1480:Thanks for creating
1308:
1282:
1271:{\displaystyle \pi }
1262:
1242:
974:
789:
695:
605:
594:{\displaystyle \pi }
585:
565:
475:
471:and the permutation
417:
298:
246:
235:{\displaystyle \pi }
226:
164:Permutation notation
46:
2272:redirect guidelines
2266:has been listed at
2110:A barnstar for you!
1396:.) And details for
2202:arbitration policy
2131:Excellent page at
2068:arbitration policy
1978:arbitration policy
1890:arbitration policy
1824:Syllogism#Examples
1817:SyllogismSentences
1749:Yours faithfully,
1585:arbitration policy
1320:
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783:you wrote this as:
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1251:{\displaystyle x}
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574:{\displaystyle x}
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18:User talk:Lipedia
16:(Redirected from
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2286:it has begun...
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1807:SyllogismImages
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1699:SyllogismImages
1695:
1687:Hi, Watchduck!
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1526:Bishal Shrestha
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104:Best regards,
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2263:COM:OVERWRITE
2260:The redirect
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1519:Page Curation
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1482:COM:OVERWRITE
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28:Empty graphs.
27:
19:
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2275:
2254:
2248:" listed at
2212:
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1524:
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1504:
1497:
1486:
1479:
1452:
1437:
1397:
1385:
1358:
1339:
1258:permuted by
1180:
581:permuted by
370:
294:actually is
242:on a vector
219:
207:
175:
171:
168:
141:
103:
100:
96:
92:
89:
85:
81:
75:
40:
34:
31:
2214:voting page
2080:voting page
1990:voting page
1902:voting page
1656:OfficialURL
1639:OfficialURL
1597:voting page
1463:Steelpillow
413:The vector
169:Dear Duck,
2282:* Pppery *
2198:topic bans
2064:topic bans
1974:topic bans
1886:topic bans
1798:) used in
1581:topic bans
384:Dear Duck,
2430:has been
2390:has been
2350:has been
2322:Jonesey95
2310:has been
2194:site bans
2060:site bans
1970:site bans
1882:site bans
1828:Watchduck
1667:Watchduck
1577:site bans
1433:Watchduck
1335:Watchduck
1176:Watchduck
366:Watchduck
121:Watchduck
1822:used in
1765:JoergenB
1751:JoergenB
1740:JoergenB
1663:this set
1455:faceting
1449:Faceting
561:Usually
212:Wcherowi
146:JoergenB
106:JoergenB
2221:NoACEMM
2087:NoACEMM
1997:NoACEMM
1909:NoACEMM
1736:history
1604:NoACEMM
1421:A300694
1411:A300693
1400:=4 are
1224:Dratman
1145:Dratman
768:Dratman
390:Dratman
216:removed
185:Dratman
2442:Gonnym
2402:Gonnym
2362:Gonnym
1728:revert
1359:About
1304:" or "
1833:quack
1672:quack
1438:quack
1340:quack
1181:quack
371:quack
126:quack
2487:talk
2446:talk
2406:talk
2366:talk
2326:talk
2320:. –
2232:talk
2184:The
2143:talk
2098:talk
2050:The
2008:talk
1960:The
1919:talk
1872:The
1812:and
1769:talk
1755:talk
1644:talk
1614:talk
1567:The
1530:talk
1511:~~~~
1500:here
1467:Talk
1428:this
1417:OEIS
1414:and
1407:OEIS
1402:here
1394:here
1390:here
1375:talk
1361:this
1228:talk
1149:talk
970:and
772:talk
394:talk
214:has
210:But
204:this
150:talk
142:Done
110:talk
36:Here
32:Hi!
2481:--
1720:not
1708:all
1371:JBL
1367:-->
779:In
601:is
181:Hi
76:not
2489:)
2448:)
2440:.
2408:)
2400:.
2368:)
2360:.
2328:)
2234:)
2223:}}
2219:{{
2196:,
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2085:{{
2062:,
2010:)
1999:}}
1995:{{
1972:,
1921:)
1911:}}
1907:{{
1884:,
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1814:{{
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1796:}}
1790:{{
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1780:{{
1771:)
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1696:{{
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1602:{{
1579:,
1532:)
1513:.
1484:.
1469:)
1419::
1409::
1377:)
1330:".
1318:π
1286:π
1266:π
1099:σ
1088:…
1071:σ
1049:σ
1035:σ
1013:…
933:−
929:σ
917:…
895:−
891:σ
863:−
859:σ
828:…
793:σ
761:.
735:π
724:…
707:π
660:−
656:π
644:…
622:−
618:π
589:π
529:π
524:…
510:π
498:…
479:π
443:…
396:)
338:π
327:…
310:π
266:…
230:π
152:)
112:)
59:∅
53:∅
2485:(
2444:(
2404:(
2364:(
2324:(
2244:"
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1917:(
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1767:(
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1716:n
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1292:x
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1246:x
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1067:x
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1038:=
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1024:n
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1010:,
1005:2
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952:)
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944:n
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936:1
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898:1
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866:1
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847:=
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812:,
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731:x
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625:1
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569:x
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