Journal of Combinatorics

Volume 11 (2020)

Number 2

Lecture hall $P$-partitions

Pages: 391 – 412

DOI: https://dx.doi.org/10.4310/JOC.2020.v11.n2.a9

Authors

Petter Brändén (Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden)

Madeleine Leander (Department of Mathematics, Stockholm University, Stockholm, Sweden)

Abstract

We introduce and study $s$-lecture hall $P$-partitions which is a generalization of $s$-lecture hall partitions to labeled (weighted) posets. We provide generating function identities for $s$-lecture hall $P$-partitions that generalize identities obtained by Savage and Schuster for $s$-lecture hall partitions, and by Stanley for $P$-partitions. We also prove that the corresponding $(P, s)$-Eulerian polynomials are real-rooted for certain pairs $(P, s)$, and speculate on unimodality properties of these polynomials.

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Petter Brändén is a Wallenberg Academy Fellow supported by the Knut and Alice Wallenberg Foundation and Vetenskapsrådet.

Received 21 February 2019

Published 14 January 2020