Enumeration of doubly up-down permutations
L. Carlitz · Pacific Journal of Mathematics · 1977
It is well known that Λ(n), the number of up-down permutations of {1,2, , n} satisfies In the present paper generating functions are obtained for up-down (down-up) permutations in which the peaks themselves are in an up-down configuration.In a previous paper the writer obtained generating functions for the number of up-down (and down-up) permutations counting the rises among the "peaks".