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arXiv · 2112.06679

Two cycle-chord graphs are $e$-positive

David G. L. Wang·Monica M. Y. Wang
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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.

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David G. L. Wang, Monica M. Y. Wang. 2021-12-13. Two cycle-chord graphs are $e$-positive. https://arxiv.org/abs/2112.06679

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