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arXiv · 2006.08418

A symmetric function of increasing forests

Alex Abreu·Antonio Nigro
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Abstract

For an indifference graph $G$ we define a symmetric function of increasing spanning forests of $G$. We prove that this symmetric function satisfies certain linear relations, which are also satisfied by the chromatic quasisymmetric function and unicellular LLT polynomials. As a consequence we give a combinatorial interpretation of the coefficients of the LLT polynomial in the elementary basis (up to a factor of a power of $(q-1)$), strengthening the description given by Alexandersson and Sulzgruber.

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Alex Abreu, Antonio Nigro. 2020-06-15. A symmetric function of increasing forests. https://doi.org/10.1017/fms.2021.33

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