Journal of Combinatorics

Volume 6 (2015)

Number 3

Hook coefficients of chromatic functions

Pages: 327 – 337

DOI: http://dx.doi.org/10.4310/JOC.2015.v6.n3.a4

Author

Ryan Kaliszewski (Department of Mathematics, Drexexl University, Philadelphia, Pennsylvania, U.S.A.)

Abstract

The chromatic symmetric function of a graph is a generalization of the chromatic polynomial. The key motivation for studying the structure of a chromatic symmetric function is to answer positivity conjectures by Stanley in 1995 and Gasharov in 1996. As a symmetric function one can write the chromatic symmetric function in the basis of Schur functions. In this paper we address the positivity of the Schur coefficients when the parameter of the Schur function is a hook shape. Furthermore, we explore the hook coefficients of the chromatic quasisymmetric function introduced by Shareshian and Wachs in 2014 when expanded in the (Gessel) fundamental basis.

Keywords

chromatic, symmetric, Schur, positivity

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