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 |
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Pages (from-to) | 495-514 |
Number of pages | 20 |
Journal | Journal of Algebraic Combinatorics |
Volume | 57 |
Issue number | 2 |
DOIs | |
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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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