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

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

Bibliographical note

Publisher Copyright:
© FPSAC 2019 - 31st International Conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.

Funding

∗[email protected]. Partially supported by an MIT-Israel MISTI grant and by the Israel Foundation, grant no. 1970/18. †[email protected]. Partially supported by Simons Foundation Grant #427060. ‡[email protected]. Partially supported by NSF grant DMS-1601961. §[email protected]. Partially supported by an MIT-Israel MISTI grant and by the Israel Foundation, grant no. 1970/18.

Funders	Funder number
Israel Foundation	1970/18
National Science Foundation	DMS-1601961
Simons Foundation	427060

Cite this

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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.",

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AU - Roichman, Yuval

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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.

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Cyclic quasi-symmetric functions

Abstract

Conference

Bibliographical note

Funding

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