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^*

^*此作品的通讯作者

Southern University of Science and Technology
Xi'an Jiaotong University
Beijing Institute of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

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.

源语言	英语
文章编号	114723
期刊	Discrete Mathematics
卷	349
期	1
DOI	https://doi.org/10.1016/j.disc.2025.114723
出版状态	已出版 - 1月 2026
已对外发布	是

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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.\}",

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

year = "2026",

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doi = "10.1016/j.disc.2025.114723",

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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

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SN - 0012-365X

VL - 349

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1

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ER -

Clocks are e-positive

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