All Cycle-Chords are e-Positive

David G.L. Wang

doi:10.1007/s00026-025-00753-2

All Cycle-Chords are e-Positive

David G.L. Wang^*

^*Corresponding author for this work

School of Mathematics and Statistics

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

4 Citations (Scopus)

Abstract

We establish the e-positivity of cycle-chord graphs using the composition method which is developed by Zhou and the author recently. Our method is simpler than the (e)-positivity approach which is used for handling cycle-chords with girth at most 4. We also provide a combinatorial interpretation of the e-coefficients, and conjecture the e-positivity of theta graphs.

Original language	English
Article number	111728
Journal	Annals of Combinatorics
DOIs	https://doi.org/10.1007/s00026-025-00753-2
Publication status	Accepted/In press - 2025

Keywords

Chromatic symmetric functions
Combinatorial interpretation
e-Positivity
Theta graphs

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10.1007/s00026-025-00753-2

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title = "All Cycle-Chords are e-Positive",

abstract = "We establish the e-positivity of cycle-chord graphs using the composition method which is developed by Zhou and the author recently. Our method is simpler than the (e)-positivity approach which is used for handling cycle-chords with girth at most 4. We also provide a combinatorial interpretation of the e-coefficients, and conjecture the e-positivity of theta graphs.",

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N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

PY - 2025

Y1 - 2025

N2 - We establish the e-positivity of cycle-chord graphs using the composition method which is developed by Zhou and the author recently. Our method is simpler than the (e)-positivity approach which is used for handling cycle-chords with girth at most 4. We also provide a combinatorial interpretation of the e-coefficients, and conjecture the e-positivity of theta graphs.

AB - We establish the e-positivity of cycle-chord graphs using the composition method which is developed by Zhou and the author recently. Our method is simpler than the (e)-positivity approach which is used for handling cycle-chords with girth at most 4. We also provide a combinatorial interpretation of the e-coefficients, and conjecture the e-positivity of theta graphs.

KW - Chromatic symmetric functions

KW - Combinatorial interpretation

KW - e-Positivity

KW - Theta graphs

UR - https://www.scopus.com/pages/publications/105001505957

U2 - 10.1007/s00026-025-00753-2

DO - 10.1007/s00026-025-00753-2

M3 - Article

AN - SCOPUS:105001505957

SN - 0218-0006

JO - Annals of Combinatorics

JF - Annals of Combinatorics

M1 - 111728

ER -

All Cycle-Chords are e-Positive

Abstract

Keywords

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