Results 41 to 50 of about 156 (150)
Splines, lattice points, and (arithmetic) matroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Let $X$ be a $(d \times N)$-matrix. We consider the variable polytope $\Pi_X(u) = \left\{ w \geq 0 : Xw = u \right\}$. It is known that the function $T_X$ that assigns to a parameter $u \in \mathbb{R}^N$ the volume of the polytope $\Pi_X(u)$ is piecewise
Matthias Lenz
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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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, 2022 18 pages, 6 figures. This is a draft of a chapter for the Handbook on the Tutte Polynomial. Comments are welcome!
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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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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 ...
Jordan Awan, Olivier Bernardi
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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
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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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An inequality for Tutte polynomials [PDF]
Combinatorica, 2010 The Tutte polynomial of the graph \(G=(V,E)\) can be defined by the closed formula \[ TG(x, y) =\sum_{A\subseteq E} (x - 1)^{r(E)-r(A)}(y - 1)^{| A| -r(A)} \] where \(r(A)=| V | -\omega (V,A)\), and \(\omega(V,A)\) denotes the number of components in the graph \((V,A)\). The author proves that, for a graph \(G\) without loops or bridges and \(a\), \(b\)
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Formulas for the computation of the Tutte polynomial of graphs with parallel classes
Electronic Journal of Graph Theory and Applications, 2018 We give some reduction formulas for computing the Tutte polynomial of any graph with parallel classes. Several examples are given to illustrate our results.
Eunice Mphako-Banda, Julian A. Allagan
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