Results 41 to 50 of about 6,580 (165)
The Chip Firing Game and Matroid Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this paper we construct from a cographic matroid M, a pure multicomplex whose degree sequence is the h―vector of the the matroid complex of M. This result provesa conjecture of Richard Stanley [Sta96] in the particular case of cographic matroids.
Criel Merino
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A study about the Tutte polynomials of benzenoid chains
Topological Algebra and its Applications, 2017 The Tutte polynomials for signed graphs were introduced by Kauffman. In 2012, Fath-Tabar, Gholam-Rezaeı and Ashrafı presented a formula for computing Tutte polynomial of a benzenoid chain. From this point on, we have also calculated the Tutte polynomials
Sahin Abdulgani
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Colored Tutte polynomials and composite knots [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Surveying the results of three recent papers and some currently ongoing research, we show how a generalization of Brylawski's tensor product formula to colored graphs may be used to compute the Jones polynomial of some fairly complicated knots and, in ...
Gábor Hetyei +2 more
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Galois groups of multivariate Tutte polynomials [PDF]
, 2011 The multivariate Tutte polynomial $\hat Z_M$ of a matroid $M$ is a generalization of the standard two-variable version, obtained by assigning a separate variable $v_e$ to each element $e$ of the ground set $E$. It encodes the full structure of $M$. Let $\
A.D. Sokal +7 more
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, 2023 The Tutte polynomial and Derksen's $\mathcal{G}$-invariant are the universal deletion-contraction and valuative matroid and polymatroid invariants, respectively. There are only a handful of well known invariants (like the matroid Kazhdan-Lusztig polynomials) between (in terms of fineness) the Tutte polynomial and Derksen's $\mathcal{G}$-invariant.
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Bollobás–Riordan and Relative Tutte Polynomials [PDF]
Arnold Mathematical Journal, 2015 We establish a relation between the Bollobas-Riordan polynomial of a ribbon graph with the relative Tutte polynomial of a plane graph obtained from the ribbon graph using its projection to the plane in a nontrivial way. Also we give a duality formula for the relative Tutte polynomial of dual plane graphs and an expression of the Kauffman bracket of a ...
Butler, Clark, Chmutov, Sergei
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Tutte Polynomial of Multi-Bridge Graphs [PDF]
Computer Science Journal of Moldova, 2013 In this paper, using a well-known recursion for computing the Tutte polynomial of any graph, we found explicit formulae for the Tutte polynomials of any multi-bridge graph and some $2-$tree graphs.
Julian A. Allagan
doaj
Bijections for lattice paths between two boundaries [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We prove that on the set of lattice paths with steps $N=(0,1)$ and $E=(1,0)$ that lie between two boundaries $B$ and $T$, the two statistics `number of $E$ steps shared with $B$' and `number of $E$ steps shared with $T$' have a symmetric joint ...
Sergi Elizalde, Martin Rubey
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Tutte's dichromate for signed graphs
, 2020 We introduce the ``trivariate Tutte polynomial" of a signed graph as an invariant of signed graphs up to vertex switching that contains among its evaluations the number of proper colorings and the number of nowhere-zero flows.
Goodall, Andrew +3 more
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Tutte polynomials for directed graphs
Journal of Combinatorial Theory, Series B, 2020 The Tutte polynomial is a fundamental invariant of graphs. In this article, we define and study a generalization of the Tutte polynomial for directed graphs, that we name B-polynomial. The B-polynomial has three variables, but when specialized to the case of graphs (that is, digraphs where arcs come in pairs with opposite directions), one of the ...
Awan, Jordan, Bernardi, Olivier
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