Séminaire Lotharingien de Combinatoire, 82B.6 (2019), 12 pp.

Ira M. Gessel and Yan Zhuang

Homomorphisms on noncommutative symmetric functions and permutation enumeration

Abstract. We present a unifying framework for deriving permutation enumeration formulas involving restrictions on descent compositions or permutation statistics describable in terms of descent compositions: these formulas can be proven by first lifting them to the algebra of noncommutative symmetric functions and then applying an appropriate homomorphism. We give several applications of this method including rederivations and extensions of classical results in the literature as well as new results.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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