Counting up-up-or-down-down permutations
Ira M. Gessel · arXiv (Cornell University) · 2024
Answering a question of Donald Knuth, we find the bivariate exponential generating function for "up-up-or-down-down'' permutations of odd length according to their last entry. An up-up-or-down-down permutation is a permutation $a_1a_2\cdots a_n$ satisfying $a_{2i-1}