Cyclic quasi-symmetric functions

Ron M. Adin; Ira M. Gessely; Victor Reinerz; Yuval Roichman

Cyclic quasi-symmetric functions

Ron M. Adin, Ira M. Gessely, Victor Reinerz, Yuval Roichman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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
Article number	#67
Journal	Seminaire Lotharingien de Combinatoire
Issue number	82
State	Published - 2019

Bibliographical note

Publisher Copyright:
© 2019,Seminaire Lotharingien de Combinatoire. 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. Partially supported by an MIT-Israel MISTI grant and by the Israel Science Foundation, grant no. 1970/18.Partially supported by Simons Foundation Grant #427060.Partially supported by NSF grant DMS-1601961.Partially supported by an MIT-Israel MISTI grant and by the Israel Science Foundation, grant no. 1970/18.

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

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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Cyclic quasi-symmetric functions

Abstract

Bibliographical note

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