The peak statistics on simsun permutations
  In this paper, we study the relationship among left peaks, interior peaks and up-down runs of simsun permutations. Properties of the generating polynomials, including the recurrence relation, generating function and real-rootedness are studied. Moreover, we introduce and study simsun permutations of the second kind. 
Shi-Mei Ma, Yeong-Nan Yeh
math.CO