Related papers: A recursive definition for the polymatroid Tutte p…
The configuration of a matroid $M$ is the abstract lattice of cyclic flats (flats that are unions of circuits) where we record the size and rank of each cyclic flat, but not the set. One can compute the Tutte polynomial of $M$, and stronger…
We introduce and study filtrations of a matroid on a linearly ordered ground set, which are particular sequences of nested sets. A given basis can be decomposed into a uniquely defined sequence of bases of minors, such that these bases have…
We prove that the Tutte polynomial of a coloopless paving matroid is convex along the portions of the line segments x+y=p lying in the positive quadrant. Every coloopless paving matroids is in the class of matroids which contain two…
Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a hypertoric arrangement can be computed in terms of its arithmetic Tutte polynomial.…
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…
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 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 prove some variants of the exponential formula and apply them to the multivariate Tutte polynomials (also known as Potts-model partition functions) of graphs. We also prove some further identities for the multivariate Tutte polynomial,…
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…
A common generalization for the chromatic polynomial and the flow polynomial of a graph $G$ is the Tutte polynomial $T(G;x,y)$. The combinatorial meaning for the coefficients of $T$ was discovered by Tutte at the beginning of its…
We introduce the notion of an arithmetic matroid, whose main example is given by a list of elements of a finitely generated abelian group. In particular we study the representability of its dual, providing an extension of the Gale duality…
A generalization of Tutte polynomial involved in the evaluation of the moments of the integrated geometric Brownian in the Ito formalism is discussed. The new combinatorial invariant depends on the order in which the sequence of…
We define and study the Tutte polynomial of a hyperplane arrangement. We introduce a method for computing it by solving an enumerative problem in a finite field. For specific arrangements, the computation of Tutte polynomials is then…
This is a chapter destined for the book "Handbook of the Tutte Polynomial". The chapter is a composite. The first part is a brief introduction to Orlik-Solomon algebras. The second part sketches the theory of evaluative functions on matroid…
We give explicit recursive constructions for the polytope of all matroids $\Omega_{r,n}$ in ranks 2 and 3 for all ground set sizes. This polytope was introduced in recent work by Ferroni and Fink as a tool for checking positivity…
We consider the Tutte polynomial of three classes of greedoids: those arising from rooted graphs, rooted digraphs and binary matrices. We establish the computational complexity of evaluating each of these polynomials at each fixed rational…
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…
The catenary data of a matroid $M$ of rank $r$ on $n$ elements is the vector $(\nu(M;a_0,a_1,\ldots,a_r))$, indexed by compositions $(a_0,a_1,\ldots,a_r)$, where $a_0 \geq 0$,\, $a_i > 0$ for $i \geq 1$, and $a_0+ a_1 + \cdots + a_r = n$,…
Using Tutte's combinatorial definition of a map we define a $\Delta$-matroid purely combinatorially and show that it is identical to Bouchet's topological definition.
There are several different extensions of the Tutte polynomial to graphs embedded in surfaces. To help frame the different options, here we consider the problem of extending the Tutte polynomial to cellularly embedded graphs starting from…