Some combinatorics related to central binomial coefficients: Grand-Dyck paths, coloured noncrossing partitions and signed pattern avoiding permutations

摘要

We give some interpretations to certain integer sequences in terms ofparameters on Grand-Dyck paths and coloured noncrossing partitions, and we findsome new bijections relating Grand-Dyck paths and signed pattern avoidingpermutations. Next we transfer a natural distributive lattice structure onGrand-Dyck paths to coloured noncrossing partitions and signed pattern avoidingpermutations, thus showing, in particular, that it is isomorphic to thestructure induced by the (strong) Bruhat order on a certain set of signedpattern avoiding permutations.