A categorification for the Tutte polynomial
نویسندگان
چکیده
منابع مشابه
On 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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Let M be a finite matroid with rank function r. We will write A M when we mean that A is a subset of the ground set of M, and write M|A and M A for the matroids obtained by restricting M to A and contracting M on A respectively. Let M* denote the dual matroid to M. (See [1] for definitions). The main theorem is Theorem 1. The Tutte polynomial TM(x, y) satisfies TM(x, y)= : A M TM|A(0, y) TM A(x...
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For each graph and each positive integer n, we define a chain complex whose graded Euler characteristic is equal to an appropriate nspecialization of the dichromatic polynomial. This also gives a categorification of n-specializations of the Tutte polynomial of graphs. Also, for each graph and integer n ≤ 2, we define the different one variable n-specializations of the dichromatic polynomials, a...
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2 Preliminaries 5 2.1 The ring R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 The algebra A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Algebra A and (1+1)-dimensional cobordisms . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Kauffman bracket . . . . . . . . . . . . . . . . . . . ...
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This is a close approximation to the content of my lecture. After a brief survey of well known properties, I present some new interpretations relating to random graphs, lattice point enumeration, and chip firing games. I then examine complexity issues and concentrate in particular, on the existence of randomized approximation schemes. © 1999 John Wiley & Sons, Inc. Random Struct. Alg., 15, 210–...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2006
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2006.6.2031