Schur-positivity via products of grid classes

Sergi Elizalde; Yuval Roichman

Schur-positivity via products of grid classes

Sergi Elizalde, Yuval Roichman

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Conference article › peer-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 language	English
Pages (from-to)	443-454
Number of pages	12
Journal	DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
State	Published - 2016
Event	28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016 - Vancouver, Canada Duration: 4 Jul 2016 → 8 Jul 2016

Keywords

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

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science
Discrete Mathematics and Combinatorics

Cite this

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title = "Schur-positivity via products of grid classes",

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.",

keywords = "Arc permutation, Descent, Grid class, Kronecker product, Quasisymmetric function, Schur-positivity, Symmetric group",

author = "Sergi Elizalde and Yuval Roichman",

note = "Publisher Copyright: {\textcopyright} 2014 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France; 28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016 ; Conference date: 04-07-2016 Through 08-07-2016",

year = "2016",

language = "الإنجليزيّة",

pages = "443--454",

journal = "DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE",

issn = "1462-7264",

publisher = "Maison de l'informatique et des mathematiques discretes",

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T1 - Schur-positivity via products of grid classes

AU - Elizalde, Sergi

AU - Roichman, Yuval

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Arc permutation

KW - Descent

KW - Grid class

KW - Kronecker product

KW - Quasisymmetric function

KW - Schur-positivity

KW - Symmetric group

UR - http://www.scopus.com/inward/record.url?scp=85082983128&partnerID=8YFLogxK

M3 - مقالة من مؤنمر

SN - 1462-7264

SP - 443

EP - 454

JO - DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE

JF - DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE

T2 - 28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016

Y2 - 4 July 2016 through 8 July 2016

ER -

Schur-positivity via products of grid classes

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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