Permutation statistics related to a class of noncommutative symmetric functions and generalizations of the Genocchi numbers

Abstract

We prove conjectures of the third author [L. Tevlin, Proc. FPSAC'07, Tianjin] on two new bases of noncommutative symmetric functions: the transition matrices from the ribbon basis have nonnegative integral coefficients. This is done by means of two composition-valued statistics on permutations and packed words, which generalize the combinatorics of Genocchi numbers.

13 pages

References in corpus (1)

• Polynomial realizations of some trialgebras

Cited by in corpus (1)

• Combinatorial Hopf algebras, noncommutative Hall-Littlewood functions, and permutation tableaux