Results 61 to 70 of about 495 (157)
Valuative invariants for large classes of matroids
Journal of the London Mathematical Society, Volume 110, Issue 3, September 2024.Abstract We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a stressed subset. This framework provides a new combinatorial characterization of the class of (elementary) split matroids.
Luis Ferroni, Benjamin Schröter
wiley +1 more source
European Journal of CombinatoricsThe classical Tutte polynomial is a two-variate polynomial $T_G(x,y)$ associated to graphs or more generally, matroids. In this paper, we introduce a polynomial $\widetilde{T}_H(x,y)$ associated to a bipartite graph $H$ that we call the permutation Tutte polynomial of the graph $H$.
Csongor Beke +3 more
openaire +3 more sources
Fourientation activities and the Tutte polynomial [PDF]
European Journal of Combinatorics, 2018 A fourientation of a graph G is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. We may naturally view fourientations as a mixture of subgraphs and graph orientations where unoriented and bioriented edges play the role of absent and present subgraph edges, respectively.
Spencer Backman +2 more
openaire +5 more sources
Mesh Parameterization Meets Intrinsic Triangulations
Computer Graphics Forum, Volume 43, Issue 5, August 2024.Abstract A parameterization of a triangle mesh is a realization in the plane so that all triangles have positive signed area. Triangle mesh parameterizations are commonly computed by minimizing a distortion energy, measuring the distortions of the triangles as they are mapped into the parameter domain.
Koray Akalin +3 more
wiley +1 more source
Harmonic Tutte polynomials of matroids
, 2022 In the present paper, we introduce the concept of harmonic Tutte polynomials of matroids and discuss some of their properties. In particular, we generalize Greene's theorem, thereby expressing harmonic weight enumerators of codes as evaluations of ...
Oura, Manabu +2 more
core
Polynomials and graph homomorphisms
, 2022 We develop in the language of graph homomorphisms the connection between the Tutte polynomial and the state models of statistical physics. • The Tutte polynomial and homomorphism numbers. • Spin models and edge coloring models.
Regts, Guus +3 more
core
K-theoretic Tutte polynomials of morphisms of matroids
, 2021 We generalize the Tutte polynomial of a matroid to a morphism of matroids via the K-theory of flag varieties. We introduce two different generalizations, and demonstrate that each has its own merits, where the trade-off is between the ease of ...
Dinu, R. +7 more
core +1 more source
The Electronic Journal of CombinatoricsThe 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.
openaire +2 more sources
Weak maps and the Tutte polynomial
Advances in Applied MathematicsLet $M$ and $N$ be matroids such that $N$ is the image of $M$ under a rank-preserving weak map. Generalizing results of Lucas, we prove that, for $x$ and $y$ positive, $T(M;x,y)\geq T(N;x,y)$ if and only if $x+y\geq xy$ or $M\cong N$. We give a number of consequences of this result.
Christine Cho, James G. Oxley
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Tutte and Jones polynomials of link families
, 2010 This article contains general formulas for the Tutte and Jones polynomials of families of knots and links given in Conway notation and the corresponding plots of zeroes for the Jones polynomials.
Radmila Sazdanovic +2 more
core +1 more source