arXiv:2301.08933 Abstract | arXiv Analytics

arXiv:2301.08933 [math.CO]Abstract References Reviews Resources

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

Published 2023-01-21Version 1

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.

Comments: An extended abstract of this work with fewer results and a different title is available at arXiv:2011.15080v2

Categories: math.CO

Keywords: combinatorial formula, melting lollipops, spanning trees, unicellular llt cumulants, general positivity question

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