Clocks are e-positive

L. Chen; Y. T. He; David G.L. Wang

doi:10.1016/j.disc.2025.114723

Clocks are e-positive

L. Chen
, Y. T. He
, David G.L. Wang^*

^*Corresponding author for this work

Southern University of Science and Technology
School of Mathematics and Statistics
Beijing Institute of Technology

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

Abstract

Along with his confirmation of the e-positivity of all cycle-chord graphs θ_ab1, the third author conjectured the e-positivity of all theta graphs θ_abc. In this paper, we establish the e-positivity of all clock graphs θ_ab2 by using the composition method. The key idea is to investigate the fibers of certain partial reversal transformation on compositions with all parts at least 2.

Original language	English
Article number	114723
Journal	Discrete Mathematics
Volume	349
Issue number	1
DOIs	https://doi.org/10.1016/j.disc.2025.114723
Publication status	Published - Jan 2026
Externally published	Yes

Keywords

Chromatic symmetric function
Stanley–Stembridge conjecture
The composition method
e-expansion
e-positivity

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10.1016/j.disc.2025.114723

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title = "Clocks are e-positive",

abstract = "Along with his confirmation of the e-positivity of all cycle-chord graphs θab1, the third author conjectured the e-positivity of all theta graphs θabc. In this paper, we establish the e-positivity of all clock graphs θab2 by using the composition method. The key idea is to investigate the fibers of certain partial reversal transformation on compositions with all parts at least 2.",

keywords = "Chromatic symmetric function, Stanley–Stembridge conjecture, The composition method, e-expansion, e-positivity",

author = "L. Chen and He, \{Y. T.\} and Wang, \{David G.L.\}",

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AU - Chen, L.

AU - He, Y. T.

AU - Wang, David G.L.

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N2 - Along with his confirmation of the e-positivity of all cycle-chord graphs θab1, the third author conjectured the e-positivity of all theta graphs θabc. In this paper, we establish the e-positivity of all clock graphs θab2 by using the composition method. The key idea is to investigate the fibers of certain partial reversal transformation on compositions with all parts at least 2.

AB - Along with his confirmation of the e-positivity of all cycle-chord graphs θab1, the third author conjectured the e-positivity of all theta graphs θabc. In this paper, we establish the e-positivity of all clock graphs θab2 by using the composition method. The key idea is to investigate the fibers of certain partial reversal transformation on compositions with all parts at least 2.

KW - Chromatic symmetric function

KW - Stanley–Stembridge conjecture

KW - The composition method

KW - e-expansion

KW - e-positivity

UR - https://www.scopus.com/pages/publications/105013108388

U2 - 10.1016/j.disc.2025.114723

DO - 10.1016/j.disc.2025.114723

M3 - Article

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SN - 0012-365X

VL - 349

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1

M1 - 114723

ER -

Clocks are e-positive

Abstract

Keywords

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