Consecutive Up-Down Patterns in Up-Down Permutations
Consecutive Up-Down Patterns in Up-Down Permutations
In this paper, we study the distribution of the number of consecutive pattern matches of the five up-down permutations of length four, $1324$, $2314$, $2413$, $1432$, and $3412$, in the set of up-down permutations. We show that for any such $\tau$, the generating function for the distribution of the number …