Cyclic quasi-symmetric functions

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

Research output: Contribution to journalConference articlepeer-review


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 λ, the coefficients in the expansion of the Schur function sλ 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 languageAmerican English
Article number67
Number of pages12
JournalSeminaire Lotharingien de Combinatoire
StatePublished - 2020


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