Symmetric function generalizations of graph polynomials

2001/03/30 by Timothy Y. Chow, Chow, Timothy Y. · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Graph theory and applications #math.CO #msc:05C15 #msc:05C20 #msc:05E05

paper · pdf · doi:10.48550/arxiv.math/0103229

70 pages. This is not a new paper; it is my 1995 Ph.D. thesis

arxiv created 2001/03/30 · arxiv updated 2009/11/30

Abstract

In Chapter 2 we study the path-cycle symmetric function of a digraph, a symmetric function generalization of Chung and Graham's cover polynomial. Most of this material appears in either Advances in Math. 118 (1996), 71-98 or J. Algebraic Combin. 10 (1999), 227-240. Chapter 3 contains miscellaneous results about Stanley's symmetric function generalization X_G of the chromatic polynomial, e.g., we establish a connection with some of Tutte's work on the chromatic polynomial and use this to prove that X_G is reconstructible. Most of Chapter 3 does not appear elsewhere.

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• A directed graph generalization of chromatic quasisymmetric functions

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