2007/03/04 by Dominique Foata, Foata, Dominique, Guo-Niu Han +1
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.math/0703099
arxiv created 2007/03/04 · openalex publication_date 2007/03/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct two bijections of the symmetric group Sn onto itself that enable us to show that three new three-variable statistics are equidistributed with classical statistics involving the number of fixed points. The first one is equidistributed with the triplet (fix,des,maj), the last two with (fix,exc,maj), where "fix," "des," "exc" and "maj" denote the number of fixed points, the number of descents, the number of excedances and the major index, respectively.