Sergi Elizalde ; Yuval Roichman - Schur-positivity via products of grid classes

dmtcs:6373 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) - https://doi.org/10.46298/dmtcs.6373
Schur-positivity via products of grid classesArticle

Authors: Sergi Elizalde 1; Yuval Roichman 2

  • 1 Department of Mathematics [Dartmouth]
  • 2 Department of Mathematics [Bar-Ilan]

Characterizing sets of permutations whose associated quasisymmetric function is symmetric and Schur- positive is a long-standing problem in algebraic combinatorics. In this paper we present a general method to construct Schur-positive sets and multisets, based on geometric grid classes and the product operation. Our approach produces many new instances of Schur-positive sets, and provides a broad framework that explains the existence of known such sets that until now were sporadic cases.


Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Imported on: July 4, 2016
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]

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