Combinatorics of simple marked mesh patterns in 132-avoiding permutations

International audienceWe present some combinatorial interpretations for coefficients appearing in series partitioning the permutations avoiding 132 along marked mesh patterns. We study patterns in which only one parameter is non zero the combinatorial family in bijection with 132-avoiding permutations and also preserving the statistic counted by the marked mesh pattern. Following the works of Kitaev, Remmel and Tiefenbruck, we present alternative proofs for two quadrants and give a combinatorial interpretation for the last one exhibiting a new bijection between 132-avoiding permutations and non-decreasing parking functions