Permutations with few inversions

2023/05/16 by Anders Claesson, Claesson, Anders, Atli Fannar Franklín +3
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2305.09457

openalex publication_date 2023/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A curious generating function S₀(x) for permutations of [n] with exactly n inversions is presented. Moreover, (xC(x))ⁱS₀(x) is shown to be the generating function for permutations of [n] with exactly n-i inversions, where C(x) is the generating function for the Catalan numbers.

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