Search results for "Excedence"

Statistics-preserving bijections between classical and cyclic permutations

2012

Recently, Elizalde (2011) [2] has presented a bijection between the set C"n"+"1 of cyclic permutations on {1,2,...,n+1} and the set of permutations on {1,2,...,n} that preserves the descent set of the first n entries and the set of weak excedances. In this paper, we construct a bijection from C"n"+"1 to S"n that preserves the weak excedance set and that transfers quasi-fixed points into fixed points and left-to-right maxima into themselves. This induces a bijection from the set D"n of derangements to the set C"n"+"1^q of cycles without quasi-fixed points that preserves the weak excedance set. Moreover, we exhibit a kind of discrete continuity between C"n"+"1 and S"n that preserves at each s…