%0 Journal Article
%T Enumeration of permutations by number of cyclic occurrence of peaks and valleys
%A Shi-Mei Ma
%A Chak-On Chow
%J Mathematics
%D 2012
%I arXiv
%X In this paper, we focus on the enumeration of permutations by number of cyclic occurrence of peaks and valleys. We find several recurrence relations involving the number of permutations with a prescribed number of cyclic peaks, cyclic valleys, fixed points and cycles. Several associated permutation statistics and the corresponding generating functions are also studied. In particular, we establish a connection between cyclic valleys and Pell numbers as well as cyclic peaks and alternating runs.
%U http://arxiv.org/abs/1203.6264v2