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There are several ways of defining the Tutte polynomial, for example one might start from the contraction-deletion definition. For some of these definitions there are choices, for example, the order of edges to operate on, which make it non-obvious that the answer is well-defined, in the sense of
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being independent of the various choices. Starting from the
Whitney rank polynomial definition makes it clear that it is well-defined, because there are no choices to make, hence the comment in the text. Of course it is now not obvious that it is a contraction-deletion invariant.
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The current text about the hyperbola xy=1 is completely at odds with Propos 1 of , which in a later example clearly states that V_{D(G)}( s ) = ( s^{-1/2} + s^{1/2} )^{|E|-|V|+1} s^{1-|E|-|V|} T_G( s^2, (s^2+1)/(s^2-s) ).
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859:-definedness in the definition? There is no choice of representatives being made nor anyting that would potentially make the definition ambigous. Instead, I suggets it should be mentioned that the
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has only finitely many summands (hence indeed produces a polynomial) because the graph is finite. Or maybe this was what was meant with well-definedness in this context?--
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736:{\displaystyle Z(G)=2\left(e^{-\alpha }\right)^{|E|-r(E)}\left(4\sinh \alpha \right)^{r(E)}T_{G}\left(\coth \alpha ,e^{2\alpha }\right).}
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related articles on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Francois Jaeger, Tutte
Polynomials and Link polynomials, Proc. Am. Math. Soc. Vol 103, No 2, June 1988
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on
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829:{\displaystyle Z(G)=\left(2e^{-\alpha }\right)^{|E|-r(E)}\cdots }
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Find pictures for the biographies of computer scientists (see
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Looks ok to me. What, specifically, do you see wrong? ā
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Isn't the bit about the Jones polynomial all wrong?
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