Related papers: Topological Tutte Polynomial
The Tutte polynomial is a powerfull analytic tool to study the structure of planar graphs. In this paper, we establish some relations between the number of clusters per bond for planar graph and its dual : these relations bring into play…
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
We prove an extension of the Thue-Vinogradov Lemma and show some applications. This paper is another example for the application of the polynomial method.
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…
We introduce and investigate multivariate Tutte polynomials, dichromatic polynomials, subset-corank polynomials, size-corank polynomials, and rank generating polynomials of semimatroids, which generalize the corresponding polynomial…
Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.
We introduce a new graph polynomial in two variables. This ``interlace'' polynomial can be computed in two very different ways. The first is an expansion analogous to the state space expansion of the Tutte polynomial; the significant…
The 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…
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…
The topological classification of all known non-magnetic crystalline compounds is now complete, revealing thousands of new candidate topological materials waiting to be explored in the lab.
In this article, we survey the the recent literature surrounding the geometry of complex polynomials. Specific areas surveyed are i) Generalizations of the Gauss--Lucas Theorem, ii) Geometry of Polynomials Level Sets, and iii) Shape…
This is a survey on extended affine Lie algebras and related types of Lie algebras, which generalize affine Lie algebras.
The theory of polynomials orthogonal with respect to one inner product is classical. We discuss the extension of this theory to multiple inner products. Examples include the Lam\'e and Heine-Stieltjes polynomials.
The classical relationship between the Tutte polynomial of graph theory and the Potts model of statistical mechanics has resulted in valuable interactions between the disciplines. Unfortunately, it does not include the external magnetic…
In this note we generalize the convolution formula for the Tutte polynomial of Kook-Reiner-Stanton and Etienne-Las Vergnas to a more general setting that includes both arithmetic matroids and delta-matroids. As corollaries, we obtain new…
This is a short survey illustrating some of the essential aspects of the theory of canonical extensions. In addition some topological results about canonical extensions of lattices with additional operations in finitely generated varieties…
In the paper [Proceedings of the Japan Academy, Ser. A Mathematical Sciences, 95(10) 111-113], the authors introduce the concept of the Tutte polynomials of genus $g$ and announce that each matroid $M$ can be reconstructed from its Tutte…
An observation on Hall-Littlewood polynomials.
In this note, we investigate some topological properties of probabilistic modular spaces.
Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…