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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