Related papers: Tutte polynomials for regular oriented matroids
We follow the example of Tutte in his construction of the dichromate of a graph (that is, the Tutte polynomial) as a unification of the chromatic polynomial and the flow polynomial in order to construct a new polynomial invariant of maps…
We prove several theorems concerning Tutte polynomials $T(G,x,y)$ for recursive families of graphs. In addition to its interest in mathematics, the Tutte polynomial is equivalent to an important function in statistical physics, the Potts…
The Tutte polynomial for matroids is not directly applicable to polymatroids. For instance, deletion-contraction properties do not hold. We construct a polynomial for polymatroids which behaves similarly to the Tutte polynomial of a…
Originally in 1954 the Tutte polynomial was a bivariate polynomial associated to a graph in order to enumerate the colorings of this graph and of its dual graph at the same time. However the Tutte polynomial reveals more of the internal…
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…
We introduce the active partition of the ground set of an oriented matroid perspective (or quotient, or strong map) on a linearly ordered ground set. The reorientations obtained by arbitrarily reorienting parts of the active partition share…
In this study, we present two results that relate Tutte polynomials. First, we provide new and complete polynomial invariants for graphs. We note that the number of variables of our polynomials is one. Second, let L_1 and L_2 be two…
We give a convolution formula for the Tutte polynomial T_M (x,y) of a matroid M.
We give an analogue of the Tutte polynomial for hypermaps. This polynomial can be defined as either a sum over subhypermaps, or recursively through deletion-contraction reductions where the terminal forms consist of isolated vertices. Our…
From the configuration of a matroid (which records the size and rank of the cyclic flats and the containments among them, but not the sets), one can compute several much-studied matroid invariants, including the Tutte polynomial and a…
We show how the Tutte polynomial of a matroid $M$ can be computed from its condensed configuration, which is a statistic of its lattice of cyclic flats. The results imply that the Tutte polynomial of $M$ is already determined by the…
We introduce and study the notion of the $G$-Tutte polynomial for a list $\mathcal{A}$ of elements in a finitely generated abelian group $\Gamma$ and an abelian group $G$, which is defined by counting the number of homomorphisms from…
In a recent paper, we studied the interaction between the automorphism group of a graph and its Tutte polynomial. More precisely, we proved that certain symmetries of graphs are clearly reflected by their Tutte polynomials. The purpose of…
We introduce the minor-closed, dual-closed class of multi-path matroids. We give a polynomial-time algorithm for computing the Tutte polynomial of a multi-path matroid, we describe their basis activities, and we prove some basic structural…
The multiplicity Tutte polynomial, which includes the arithmetic Tutte polynomial, is a generalization of the classical Tutte polynomial of matroids. In this paper, we obtain an expression of the general coefficient and the expressions of…
Let $T(G;X,Y)$ be the Tutte polynomial for graphs. We study the sequence $t_{a,b}(n) = T(K_n;a,b)$ where $a,b$ are non-negative integers, and show that for every $\mu \in \N$ the sequence $t_{a,b}(n)$ is ultimately periodic modulo $\mu$…
We begin with a review of Tutte's homotopy theory, which concerns the structure of certain graph associated to a matroid (together with some extra data). Concretely, Tutte's path theorem asserts that this graph is connected, and his…
It is well known that the 2-variable Tutte polynomials contain chromatic polynomial and flow polynomial of graphs, i.e. the cases of $y=0$ and $x=0$. In 2013, K\'{a}lm\'{a}n introduced the interior and exterior polynomials which generalized…
We introduce a new matroid (graph) invariant, the arboricity polynomial. Given a matroid, the arboricity polynomial enumerates the number of covers of the ground set by disjoint independent sets. We establish the polynomiality of the…
Multimatroids generalize matroids, delta-matroids, and isotropic systems, and transition polynomials of multimatroids subsume various polynomials for these latter combinatorial structures, such as the interlace polynomial and the…