Permutations with non-decreasing transposition arrays and pattern avoidance

Abstract

We give some results about a bijection associating each permutation with a subexcedant function (i.e., a function f : [n] ? [n] such that f(i) ? i, 1 ? i ? n). This function is related to a particular decomposition of the permutation as a product of transpositions and therefore it has been called transposition array in the literature. In particular, we identify anti-excedance positions of the permutation through its transposition array and we give an expression of the bijection in terms of the cycle structure of the permutation. We give a characterization of a family of permutations having a non-decreasing transposition array and study length 3 pattern avoidance therein.