The e-positivity of two classes of cycle-chord graphs

David G.L. Wang; Monica M.Y. Wang

doi:10.1007/s10801-022-01175-6

The e-positivity of two classes of cycle-chord graphs

David G.L. Wang, Monica M.Y. Wang^*

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

We prove Gebhard and Sagan’s (e)-positivity of the line graphs of tadpoles in noncommuting variables. This implies the e-positivity of these line graphs. We then extend this (e)-positivity result to that of certain cycle-chord graphs and derive the bivariate generating function of all cycle-chord graphs.

源语言	英语
页（从-至）	495-514
页数	20
期刊	Journal of Algebraic Combinatorics
卷	57
期	2
DOI	https://doi.org/10.1007/s10801-022-01175-6
出版状态	已出版 - 3月 2023

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Wang, D. G. L., & Wang, M. M. Y. (2023). The e-positivity of two classes of cycle-chord graphs. Journal of Algebraic Combinatorics, 57(2), 495-514. https://doi.org/10.1007/s10801-022-01175-6

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abstract = "We prove Gebhard and Sagan{\textquoteright}s (e)-positivity of the line graphs of tadpoles in noncommuting variables. This implies the e-positivity of these line graphs. We then extend this (e)-positivity result to that of certain cycle-chord graphs and derive the bivariate generating function of all cycle-chord graphs.",

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AU - Wang, Monica M.Y.

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N2 - We prove Gebhard and Sagan’s (e)-positivity of the line graphs of tadpoles in noncommuting variables. This implies the e-positivity of these line graphs. We then extend this (e)-positivity result to that of certain cycle-chord graphs and derive the bivariate generating function of all cycle-chord graphs.

AB - We prove Gebhard and Sagan’s (e)-positivity of the line graphs of tadpoles in noncommuting variables. This implies the e-positivity of these line graphs. We then extend this (e)-positivity result to that of certain cycle-chord graphs and derive the bivariate generating function of all cycle-chord graphs.

KW - Chromatic symmetric function

KW - Stanley and Stembridge’s 3+1 conjecture

KW - Symmetric functions in noncommuting variables

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The e-positivity of two classes of cycle-chord graphs

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