The Tutte polynomial of symmetric hyperplane arrangements
نویسندگان
چکیده
منابع مشابه
Tutte polynomials of hyperplane arrangements and the finite field method
The Tutte polynomial is a fundamental invariant associated to a graph, matroid, vector arrangement, or hyperplane arrangement, which answers a wide variety of questions about its underlying object. This short survey focuses on some of the most important results on Tutte polynomials of hyperplane arrangements. We show that many enumerative, algebraic, geometric, and topological invariants of a h...
متن کاملComputing the Tutte polynomial of a hyperplane arrangement
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 reduced to certain related enumerative questions. As a consequence, we obtain new formulas for the generating functions enumerating alternating trees, labelled tre...
متن کاملComputing the Tutte Polynomial of a Hyperplane Arragement
Theorem 1.1 [Zaslavsky 1975]. Let A be a hyperplane arrangement in Rn . The number of regions into which A dissects Rn is equal to (−1)χA(−1). The number of regions which are relatively bounded is equal to (−1)χA(1). Theorem 1.2 [Orlik and Solomon 1980]. Let A be a hyperplane arrangement in Cn , and let MA =Cn− ⋃ H∈A H be its complement. Then the Poincaré polynomial of the cohomology ring of MA...
متن کاملA Tutte Polynomial for Toric Arrangements
We introduce a multiplicity Tutte polynomial M(x, y), with applications to zonotopes and toric arrangements. We prove that M(x, y) satisfies a deletion-restriction recursion and has positive coefficients. The characteristic polynomial and the Poincaré polynomial of a toric arrangement are shown to be specializations of the associated polynomial M(x, y), likewise the corresponding polynomials fo...
متن کاملOn the tutte polynomial of benzenoid chains
The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this paper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2020
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216520500042