Nombre de factorisations d'un grand cycle

2003/07/10 by Philippe Biane, Biane, Philippe
Computer Science · Mathematics · #05A15 #05E05 #20B30 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR #msc:05A15 #msc:05E05 #msc:20B30

paper · pdf · doi:10.48550/arxiv.math/0307147

3 pages; in French

arxiv created 2003/07/10 · openalex publication_date 2003/07/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a short proof, based on symmetric function theory, of a formula due to Goupil and Schaeffer, counting the number of factorizations of a cycle of maximal length in the symmetric group, into the product of two permutations of given conjugacy classes.

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