  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.
