×

zbMATH — the first resource for mathematics

Permutation statistics related to a class of noncommutative symmetric functions and generalizations of the Genocchi numbers. (English) Zbl 1194.05161
Summary: We prove conjectures of the third author [L. Tevlin, “Noncommutative monomial symmetric functions”, In: Proceedings of Formal Power Series and Algebraic Combinatorics, 2007 (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.

MSC:
05E05 Symmetric functions and generalizations
15A15 Determinants, permanents, traces, other special matrix functions
11B75 Other combinatorial number theory
16T30 Connections of Hopf algebras with combinatorics
Software:
OEIS; MuPAD
PDF BibTeX XML Cite
Full Text: DOI arXiv