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arXiv · 2301.08933

A combinatorial formula for LLT cumulants of melting lollipops in terms of spanning trees

Maciej Kowalski
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Abstract

We prove a combinatorial formula for LLT cumulants of melting lollipops as a positive combination of LLT polynomials indexed by spanning trees. The result gives an affirmative answer to a general positivity question for this class of unicellular LLT cumulants, and gives an independent proof of their Schur-positivity. In the special case of the complete graph, we also express the formula in terms of parking functions.

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Maciej Kowalski. 2023-11-15. A combinatorial formula for LLT cumulants of melting lollipops in terms of spanning trees. https://arxiv.org/abs/2301.08933

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