Title: A Foata bijection for the alternating group and for q analogues
Abstract:The Foata bijection $Φ: S_n \to S_n$ is extended to the bijections $Ψ: A_{n+1} \to A_{n+1}$ and $Ψ_q : S_{n+q-1} \to S_{n+q-1}$, where S_m, A_m are the symmetric and the alternating groups. These bije...The Foata bijection $Φ: S_n \to S_n$ is extended to the bijections $Ψ: A_{n+1} \to A_{n+1}$ and $Ψ_q : S_{n+q-1} \to S_{n+q-1}$, where S_m, A_m are the symmetric and the alternating groups. These bijections imply bijective proofs for recent equidistribution theorems, by Regev and Roichman, for A_{n+1} and for S_{n+q-1}.Read More