We give some interpretations to certain integer sequences in terms of parameters on Grand-Dyck paths and coloured noncrossing partitions, and we find some new bijections relating Grand-Dyck paths and signed pattern avoiding permutations. Next we transfer a natural distributive lattice structure on Grand-Dyck paths to coloured noncrossing partitions and signed pattern avoiding permutations, thus showing, in particular, that it is isomorphic to the structure induced by the (strong) Bruhat order on a certain set of signed pattern avoiding permutations.
Some combinatorics related to central binomial coefficients: Grand-Dyck paths, coloured noncrossing partitions and signed pattern avoiding permutations / Ferrari, Luca. - In: GRAPHS AND COMBINATORICS. - ISSN 0911-0119. - STAMPA. - 26:(2010), pp. 51-70.
Some combinatorics related to central binomial coefficients: Grand-Dyck paths, coloured noncrossing partitions and signed pattern avoiding permutations
FERRARI, LUCA
2010
Abstract
We give some interpretations to certain integer sequences in terms of parameters on Grand-Dyck paths and coloured noncrossing partitions, and we find some new bijections relating Grand-Dyck paths and signed pattern avoiding permutations. Next we transfer a natural distributive lattice structure on Grand-Dyck paths to coloured noncrossing partitions and signed pattern avoiding permutations, thus showing, in particular, that it is isomorphic to the structure induced by the (strong) Bruhat order on a certain set of signed pattern avoiding permutations.File | Dimensione | Formato | |
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