Cyclic quasi-symmetric functions

Ron M. Adin; Ira M. Gessel; Victor Reiner; Yuval Roichman

Cyclic quasi-symmetric functions

Ron M. Adin, Ira M. Gessel, Victor Reiner, Yuval Roichman

Department of Mathematics

Bar-Ilan University

Research output: Contribution to conference › Paper › peer-review

Abstract

The ring of cyclic quasi-symmetric functions is introduced in this paper. A natural basis consists of fundamental cyclic quasi-symmetric functions; they arise as toric P-partition enumerators, for toric posets P with a total cyclic order. The associated structure constants are determined by cyclic shuffles of permutations. For every non-hook shape l, the coefficients in the expansion of the Schur function sl in terms of fundamental cyclic quasi-symmetric functions are nonnegative. The theory has applications to the enumeration of cyclic shuffles and SYT by cyclic descents.

Original language	English
State	Published - 2019
Event	31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019 - Ljubljana, Slovenia Duration: 1 Jul 2019 → 5 Jul 2019

Conference

Conference	31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019
Country/Territory	Slovenia
City	Ljubljana
Period	1/07/19 → 5/07/19

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Cite this

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title = "Cyclic quasi-symmetric functions",

abstract = "The ring of cyclic quasi-symmetric functions is introduced in this paper. A natural basis consists of fundamental cyclic quasi-symmetric functions; they arise as toric P-partition enumerators, for toric posets P with a total cyclic order. The associated structure constants are determined by cyclic shuffles of permutations. For every non-hook shape l, the coefficients in the expansion of the Schur function sl in terms of fundamental cyclic quasi-symmetric functions are nonnegative. The theory has applications to the enumeration of cyclic shuffles and SYT by cyclic descents.",

author = "Adin, \{Ron M.\} and Gessel, \{Ira M.\} and Victor Reiner and Yuval Roichman",

note = "Publisher Copyright: {\textcopyright} FPSAC 2019 - 31st International Conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.; 31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019 ; Conference date: 01-07-2019 Through 05-07-2019",

year = "2019",

language = "الإنجليزيّة",

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TY - CONF

T1 - Cyclic quasi-symmetric functions

AU - Adin, Ron M.

AU - Gessel, Ira M.

AU - Reiner, Victor

AU - Roichman, Yuval

PY - 2019

Y1 - 2019

N2 - The ring of cyclic quasi-symmetric functions is introduced in this paper. A natural basis consists of fundamental cyclic quasi-symmetric functions; they arise as toric P-partition enumerators, for toric posets P with a total cyclic order. The associated structure constants are determined by cyclic shuffles of permutations. For every non-hook shape l, the coefficients in the expansion of the Schur function sl in terms of fundamental cyclic quasi-symmetric functions are nonnegative. The theory has applications to the enumeration of cyclic shuffles and SYT by cyclic descents.

AB - The ring of cyclic quasi-symmetric functions is introduced in this paper. A natural basis consists of fundamental cyclic quasi-symmetric functions; they arise as toric P-partition enumerators, for toric posets P with a total cyclic order. The associated structure constants are determined by cyclic shuffles of permutations. For every non-hook shape l, the coefficients in the expansion of the Schur function sl in terms of fundamental cyclic quasi-symmetric functions are nonnegative. The theory has applications to the enumeration of cyclic shuffles and SYT by cyclic descents.

UR - http://www.scopus.com/inward/record.url?scp=85087884407&partnerID=8YFLogxK

M3 - محاضرة

T2 - 31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019

Y2 - 1 July 2019 through 5 July 2019

ER -

Cyclic quasi-symmetric functions

Abstract

Conference

All Science Journal Classification (ASJC) codes

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