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arXiv · 2410.07581

Clocks are $e$-positive

L. Chen·Y. T. He·David G. L. Wang
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Abstract

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 $2$.

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L. Chen, Y. T. He, David G. L. Wang. 2025-07-29. Clocks are $e$-positive. https://arxiv.org/abs/2410.07581

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