A Foata bijection for the alternating group and for q analogues

Details A Foata bijection for the alternating group and for q analogues A Foata bijection for the alternating group and for q analogues

2005-03-06

arxiv.org/abs/math/0503112v1

S\'eminaire Lotharingien Combin. 53 (2005), Article B53b, 16 pp

Mathematics

Combinatorics

16 pages

Scientific paper

The Foata bijection $\Phi : S_n \to S_n$ is extended to the bijections $\Psi
: A_{n+1} \to A_{n+1}$ and $\Psi_q : S_{n+q-1} \to S_{n+q-1}$, 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}.

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