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^*

^*Corresponding author for this work

School of Mathematics and Statistics

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

Abstract

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.

Original language	English
Pages (from-to)	495-514
Number of pages	20
Journal	Journal of Algebraic Combinatorics
Volume	57
Issue number	2
DOIs	https://doi.org/10.1007/s10801-022-01175-6
Publication status	Published - Mar 2023

Keywords

Chromatic symmetric function
Stanley and Stembridge’s 3+1 conjecture
Symmetric functions in noncommuting variables
e-positivity

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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.",

keywords = "Chromatic symmetric function, Stanley and Stembridge{\textquoteright}s 3+1 conjecture, Symmetric functions in noncommuting variables, e-positivity",

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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

KW - e-positivity

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IS - 2

ER -

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

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Keywords

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