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arXiv · 2408.01385

Positive $e_I$-expansions for KPKP graphs, twinned lollipops, and kayak paddles

Davion Q. B. Tang·David G. L. Wang
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Abstract

We derive explicit positive $e_I$-expansions for the chromatic symmetric functions of several graph families. First, we obtain a uniform formula for KPKP graphs that specializes to known formulas for lollipops, KPK graphs, KKP graphs, and PKP graphs. We then give positive $e_I$-expansions for twinned paths and cycles and apply the KPKP formula to twinned lollipops. Finally, we establish a positive $e_I$-expansion for kayak paddles and specialize it to infinity graphs. These formulas refine ordinary $e$-positivity by retaining composition-indexed coefficients and provide independent proofs complementary to existing recurrence, unit-interval, and noncommutative methods.

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Davion Q. B. Tang, David G. L. Wang. 2024-08-02. Positive $e_I$-expansions for KPKP graphs, twinned lollipops, and kayak paddles. https://arxiv.org/abs/2408.01385

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