Related papers: Dual complementary polynomials of graphs and combi…
The Tutte polynomial is a classical invariant, important in combinatorics and statistical mechanics. An essential feature of the Tutte polynomial is the duality for planar graphs G, $T_G(X,Y)\; =\; {T}_{G^*}(Y,X)$ where $G^*$ denotes the…
We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of We study (Galois) linear complementary dual codes over mixed alphabets arising…
In this note we study a certain graph polynomial arising from a special recursion. This recursion is a member of a family of four recursions where the other three recursions belong to the chromatic polynomial, the modified matching…
In the zero-error Slepian-Wolf source coding problem, the optimal rate is given by the complementary graph entropy $\overline{H}$ of the characteristic graph. It has no single-letter formula, except for perfect graphs, for the pentagon…
Given a polynomial map f on the Euclidean n-space and a vector q, the polynomial complementarity problem, PCP(f,q), is the nonlinear complementarity problem of finding a nonnegative vector x such that y=f(x)+q is nonnegative and orthogonal…
A generalization of Arnold's strange duality to invertible polynomials in three variables by the first author and A.Takahashi includes the following relation. For some invertible polynomials $f$ the Saito dual of the reduced monodromy zeta…
We use Young's raising operators to introduce and study double eta polynomials, which are an even orthogonal analogue of Wilson's double theta polynomials. Our double eta polynomials give Giambelli formulas which represent the equivariant…
The duality theorem of Lass relates the matching polynomials of a simple graph $G$ with the matching polynomials of its complement $\bar G$. In particular, this relation gives rise to Godsil's result, which offers a nice interpretation of…
We combinatorially prove a new recurrence between the Tutte polynomials of graphs obtained by contraction of the complete graphs $K_{n}$%. This generalizes, to two variables, a relation previously obtained by the author between the…
A famous and wide-open problem, going back to at least the early 1970's, concerns the classification of chromatic polynomials of graphs. Toward this classification problem, one may ask for necessary inequalities among the coefficients of a…
We recover the Tutte polynomial of a matroid, up to change of coordinates, from an Ehrhart-style polynomial counting lattice points in the Minkowski sum of its base polytope and scalings of simplices. Our polynomial has coefficients of…
In this work, we define an orthogonal graph on the set of equivalence classes of $(2\nu + \delta)-$tuples over $\mathbb{Z}_{2^n}$ where $n$ and $\nu$ are positive integers and $\delta = 0, 1$ or $2$. We classify our graph if it is strongly…
We consider a graph polynomial \xi(G;x,y,z) introduced by Averbouch, Godlin, and Makowsky (2007). This graph polynomial simultaneously generalizes the Tutte polynomial as well as a bivariate chromatic polynomial defined by Dohmen, Poenitz…
We introduce an arithmetic version of the multivariate Tutte polynomial, and (for representable arithmetic matroids) a quasi-polynomial that interpolates between the two. A generalized Fortuin-Kasteleyn representation with applications to…
Let $G$ be an almost simple simply connected group over complex numbers. For a positive element $\alpha$ of the coroot lattice of $G$ let $Z^\alpha$ denote the space of based maps from the projective line to the flag variety of $G$ of…
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…
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…
For a ring R, denote by Spec^R_kappa(Gamma) the kappa-spectrum of the Gamma-invariant of strongly uniform right R-modules. Recent realization techniques of Goodearl and Wehrung show that Spec^R_{aleph_1}(Gamma) is full for suitable von…
Tutte's dichromate T(x,y) is a well known graph invariant. Using the original definition in terms of internal and external activities as our point of departure, we generalize the valuations T(x,1) and T(1,y) to hypergraphs. In the…
It is shown that the fundamental group of the Griffiths double cone space is isomorphic to that of the triple cone. More generally if $\kappa$ is a cardinal such that $2 \leq \kappa \leq 2^{\aleph_0}$ then the $\kappa$-fold cone has the…