Simsun permutations, simsun successions and simsun patterns

Abstract

In this paper, we introduce the definitions of simsun succession, simsun cycle succession and simsun pattern. In particular, the ordinary simsun permutations are permutations avoiding simsun pattern 321. We study the descent and peak statistics on permutations avoiding simsun successions. We give a combinatorial interpretation of the q-Eulerian polynomials introduced by Brenti (J. Combin. Theory Ser. A 91 (2000), 137-170). We also present a bijection between permutations avoiding simsun pattern 132 and set partitions.

11 pages

References in corpus (3)

• The symmetric and unimodal expansion of Eulerian polynomials via continued fractions
• Context-free Grammars and Multivariate Stable Polynomials over Stirling Permutations
• The peak statistics on simsun permutations