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728:
576:
323:
47:
267:
128:
104:
68:
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649:
378:
363:
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Note that the empty set is a face of every polyhedron, and so the intersection of two polyhedra in
925:
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39:
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489:"Standard bases and geometric invariant theory I. Initial ideals and state polytopes"
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that fit together in a specific way. Polyhedral complexes generalize
410:, Graduate Texts in Mathematics, vol. 152, Berlin, New York:
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134:
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74:
516:
42:
and arise in various areas of polyhedral geometry, such as
199:{\displaystyle \sigma _{1},\sigma _{2}\in {\mathcal {K}}}
310:
are polyhedral complexes in which every polyhedron is a
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is a polyhedral complex in which every polyhedron is a
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107:
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252:
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373:A tropical variety obtained by tropicalizing an
300:are polyhedral complexes satisfying a certain
532:
8:
343:from the origin. Examples of fans include:
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93:that satisfies the following conditions:
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72:
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454:Mora, Teo; Robbiano, Lorenzo (1988).
7:
487:Bayer, David; Morrison, Ian (1988).
14:
430:Introduction to Tropical Geometry
899:
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493:Journal of Symbolic Computation
460:Journal of Symbolic Computation
281:{\displaystyle {\mathcal {K}}}
142:{\displaystyle {\mathcal {K}}}
118:{\displaystyle {\mathcal {K}}}
82:{\displaystyle {\mathcal {K}}}
1:
506:10.1016/S0747-7171(88)80043-9
473:10.1016/S0747-7171(88)80042-7
456:"The Gröbner fan of an ideal"
433:. American Mathematical Soc.
427:; Sturmfels, Bernd (2015).
406:Ziegler, GĂĽnter M. (1995),
253:{\displaystyle \sigma _{2}}
226:{\displaystyle \sigma _{1}}
942:
793:Banach fixed-point theorem
826:
622:
381:with trivial valuation.
52:hyperplane arrangements
848:Mathematics portal
748:Metrics and properties
734:Second-countable space
388:of a tropical variety.
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408:Lectures on Polytopes
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156:of any two polyhedra
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101:of a polyhedron from
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803:Invariance of domain
755:Euler characteristic
729:Bundle (mathematics)
308:Simplicial complexes
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160:
129:
105:
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40:simplicial complexes
813:Tychonoff's theorem
808:Poincaré conjecture
562:General (point-set)
302:balancing condition
798:De Rham cohomology
719:Polyhedral complex
709:Simplicial complex
298:Tropical varieties
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206:is a face of both
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64:polyhedral complex
25:polyhedral complex
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702:fundamental group
375:algebraic variety
44:tropical geometry
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592:low-dimensional
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368:polynomial ring
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765:Winding number
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697:homotopy group
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288:may be empty.
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775:Orientability
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611:Set-theoretic
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572:Combinatorial
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440:9780821851982
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386:recession fan
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905:Publications
770:Chern number
760:Betti number
718:
643: /
634:Key concepts
582:Differential
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379:valued field
336:
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154:intersection
89:is a set of
63:
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36:vector space
27:is a set of
24:
18:
16:Math concept
868:Wikiversity
785:Key results
360:Gröbner fan
125:is also in
21:mathematics
714:CW complex
655:Continuity
645:Closed set
604:cohomology
393:References
349:normal fan
58:Definition
926:Polyhedra
893:geometric
888:algebraic
739:Cobordism
675:Hausdorff
670:connected
587:Geometric
577:Continuum
567:Algebraic
242:σ
215:σ
187:∈
178:σ
165:σ
97:1. Every
91:polyhedra
29:polyhedra
920:Category
858:Wikibook
836:Category
724:Manifold
692:Homotopy
650:Interior
641:Open set
599:Homology
548:Topology
353:polytope
292:Examples
883:general
685:uniform
665:compact
616:Digital
377:over a
324:Splines
312:simplex
152:2. The
48:splines
878:Topics
680:metric
555:Fields
437:
362:of an
660:Space
366:of a
364:ideal
351:of a
31:in a
435:ISBN
384:The
358:The
347:The
341:cone
331:Fans
233:and
99:face
50:and
33:real
23:, a
501:doi
468:doi
337:fan
19:In
922::
495:.
491:.
462:.
458:.
335:A
62:A
54:.
46:,
540:e
533:t
526:v
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503::
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464:6
443:.
370:.
355:.
326:.
320:.
314:.
304:.
274:K
260:.
246:2
219:1
192:K
182:2
174:,
169:1
149:.
135:K
111:K
75:K
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