Séminaire Lotharingien de Combinatoire, 80B.5 (2018), 12 pp.

Ira M. Gessel and Yan Zhuang

Shuffle-Compatible Descent Statistics and Quotients of Quasisymmetric Functions

Abstract. We study shuffle-compatible permutation statistics: permutation statistics st with the property that the distribution of st over all shuffles of two permutations π and σ is completely determined by st(π), st(σ), and the lengths of π and σ. We develop a theory of shuffle-compatibility for descent statistics---permutation statistics that depend only on the descent set and length---and its connections to P-partitions, quasisymmetric functions, and noncommutative symmetric functions.

Received: November 14, 2017. Accepted: February 17, 2018. Final version: April 1, 2018.

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