Schur-positivity via products of grid classes

Sergi Elizalde, Yuval Roichman

Research output: Contribution to journalConference articlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)443-454
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2016
Event28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016 - Vancouver, Canada
Duration: 4 Jul 20168 Jul 2016

Bibliographical note

Publisher Copyright:
© 2014 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France

Funding

†Email: [email protected]. Partially supported by grant #280575 from the Simons Foundation and by grant H98230-14-1-0125 from the NSA. ‡Email: [email protected]. Partially supported by Dartmouth’s Shapiro visitors fund.

FundersFunder number
Simons FoundationH98230-14-1-0125
National Security Agency

    Keywords

    • Arc permutation
    • Descent
    • Grid class
    • Kronecker product
    • Quasisymmetric function
    • Schur-positivity
    • Symmetric group

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