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A Symmetric Function of Increasing Forests

Part of: Combinatorics Algebraic combinatorics

Published online by Cambridge University Press:  29 April 2021

Alex Abreu  and
Antonio Nigro
Alex Abreu
Affiliation:
Instituto de Matemática e Estatística, Universidade Federal Fluminense, Rua Prof. M. W. de Freitas, S/N, 24210-201 Niterói, Rio de Janeiro, Brasil; E-mail: alexbra1@gmail.com.
Antonio Nigro
Affiliation:
Instituto de Matemática e Estatística, Universidade Federal Fluminense, Rua Prof. M. W. de Freitas, S/N, 24210-201 Niterói, Rio de Janeiro, Brasil; E-mail: alexbra1@gmail.com.

Abstract

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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 $\textrm {LLT}$ polynomials. As a consequence, we give a combinatorial interpretation of the coefficients of the $\textrm {LLT}$ polynomial in the elementary basis (up to a factor of a power of $(q-1)$), strengthening the description given in [4].

MSC classification

Primary: 05A05: Permutations, words, matrices
Secondary: 05E05: Symmetric functions and generalizations
Type
Discrete Mathematics
Information
Forum of Mathematics, Sigma , Volume 9 , 2021 , e35
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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