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

^*此作品的通讯作者

数学学院

Beijing Institute of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

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摘要

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.

源语言	英语
文章编号	102886
期刊	Advances in Applied Mathematics
卷	167
DOI	http://doi.org/10.1016/j.aam.2025.102886
出版状态	已出版 - 6月 2025

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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.\}",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Inc.",

year = "2025",

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doi = "10.1016/j.aam.2025.102886",

language = "English",

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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

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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

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