A composition method for neat formulas of chromatic symmetric functions

David G.L. Wang; James Z.F. Zhou

doi:10.1016/j.aam.2025.102886

A composition method for neat formulas of chromatic symmetric functions

David G.L. Wang^*, James Z.F. Zhou

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We develop a composition method to unearth positive e_I-expansions of chromatic symmetric functions X_G, where the subscript I stands for compositions rather than integer partitions. Using this method, we derive positive and neat e_I-expansions for the chromatic symmetric functions of tadpoles, barbells and generalized bulls, and establish the e-positivity of hats. We also obtain a compact ribbon Schur analog for the chromatic symmetric function of cycles.

Original language	English
Article number	102886
Journal	Advances in Applied Mathematics
Volume	167
DOIs	http://doi.org/10.1016/j.aam.2025.102886
Publication status	Published - Jun 2025

Keywords

Chromatic symmetric functions
Noncommutative symmetric functions
Ribbon Schur functions
Schur positivity
e-Positivity

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10.1016/j.aam.2025.102886

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title = "A composition method for neat formulas of chromatic symmetric functions",

abstract = "We develop a composition method to unearth positive eI-expansions of chromatic symmetric functions XG, where the subscript I stands for compositions rather than integer partitions. Using this method, we derive positive and neat eI-expansions for the chromatic symmetric functions of tadpoles, barbells and generalized bulls, and establish the e-positivity of hats. We also obtain a compact ribbon Schur analog for the chromatic symmetric function of cycles.",

keywords = "Chromatic symmetric functions, Noncommutative symmetric functions, Ribbon Schur functions, Schur positivity, e-Positivity",

author = "Wang, \{David G.L.\} and Zhou, \{James Z.F.\}",

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AU - Zhou, James Z.F.

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N2 - We develop a composition method to unearth positive eI-expansions of chromatic symmetric functions XG, where the subscript I stands for compositions rather than integer partitions. Using this method, we derive positive and neat eI-expansions for the chromatic symmetric functions of tadpoles, barbells and generalized bulls, and establish the e-positivity of hats. We also obtain a compact ribbon Schur analog for the chromatic symmetric function of cycles.

AB - We develop a composition method to unearth positive eI-expansions of chromatic symmetric functions XG, where the subscript I stands for compositions rather than integer partitions. Using this method, we derive positive and neat eI-expansions for the chromatic symmetric functions of tadpoles, barbells and generalized bulls, and establish the e-positivity of hats. We also obtain a compact ribbon Schur analog for the chromatic symmetric function of cycles.

KW - Chromatic symmetric functions

KW - Noncommutative symmetric functions

KW - Ribbon Schur functions

KW - Schur positivity

KW - e-Positivity

UR - http://www.scopus.com/pages/publications/105001493264

U2 - 10.1016/j.aam.2025.102886

DO - 10.1016/j.aam.2025.102886

M3 - Article

AN - SCOPUS:105001493264

SN - 0196-8858

VL - 167

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

M1 - 102886

ER -

A composition method for neat formulas of chromatic symmetric functions

Abstract

Keywords

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