Counting up-up-or-down-down permutations

2024/11/25 by Ira M. Gessel, Gessel, Ira M.
Biochemistry, Genetics and Molecular Biology · Computer Science · #Algorithms and Data Compression #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #Genome Rearrangement Algorithms

paper · pdf · doi:10.48550/arxiv.2411.16113

openalex publication_date 2024/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 a₁a₂⋯ a_n satisfying a_2i-1

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