Using functional equations to enumerate 1324-avoiding permutations

2013/09/27 by Fredrik Johansson, Johansson, Fredrik, Brian Nakamura +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1309.7117

openalex publication_date 2013/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of enumerating permutations with exactly r occurrences of the pattern 1324 and derive functional equations for this general case as well as for the pattern avoidance (r=0) case. The functional equations lead to a new algorithm for enumerating length n permutations that avoid 1324. This approach is used to enumerate the 1324-avoiders up to n=31. We also extend those functional equations to account for the number of inversions and derive analogous algorithms.

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