All Cycle-Chords are e-Positive

TY - JOUR

T1 - All Cycle-Chords are e-Positive

AU - Wang, David G.L.

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 -