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 |
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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 |
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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 |
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Israel Foundation | 1970/18 |
National Science Foundation | DMS-1601961 |
Simons Foundation | 427060 |