New permutation coding and equidistribution of set-valued statistics

Dominique Foata (1) , Guo-Niu Han (1)

1 IRMA - Institut de Recherche Mathématique Avancée

A new coding for permutations is explicitly constructed and its association with the classical Lehmer coding provides a bijection of the symmetric group onto itself serving to show that six bivariable set-valued statistics are equidistributed on that group. This extends a recent result due to Cori valid for integer-valued statistics.

Domaines: Combinatoire [math.CO]; Algorithme et structure de données [cs.DS]

Dominique Foata, Guo-Niu Han. New permutation coding and equidistribution of set-valued statistics. Theoretical Computer Science, 2009, 13 p. ⟨hal-00395705⟩