In [Ferrari, L. and Pinzani, R.: Lattices of lattice paths. J. Stat. Plan. Inference 135 (2005), 77–92] a natural order on Dyck paths of any fixed length inducing a distributive lattice structure is defined. We transfer this order to noncrossing partitions along a well-known bijection [Simion, R.: Noncrossing partitions. Discrete Math. 217 (2000), 367–409], thus showing that noncrossing partitions can be endowed with a distributive lattice structure having some combinatorial relevance. Finally we prove that our lattices are isomorphic to the posets of 312- avoiding permutations with the order induced by the strong Bruhat order of the symmetric group.

A distributive lattice structure connecting Dyck paths, noncrossing partitions and 312-avoiding permutations / E. BARCUCCI; A. BERNINI; L. FERRARI; M. PONETI. - In: ORDER. - ISSN 0167-8094. - STAMPA. - 22:(2005), pp. 311-328. [10.1007/s11083-005-9021-x]

A distributive lattice structure connecting Dyck paths, noncrossing partitions and 312-avoiding permutations

BARCUCCI, ELENA;BERNINI, ANTONIO;FERRARI, LUCA;
2005

Abstract

In [Ferrari, L. and Pinzani, R.: Lattices of lattice paths. J. Stat. Plan. Inference 135 (2005), 77–92] a natural order on Dyck paths of any fixed length inducing a distributive lattice structure is defined. We transfer this order to noncrossing partitions along a well-known bijection [Simion, R.: Noncrossing partitions. Discrete Math. 217 (2000), 367–409], thus showing that noncrossing partitions can be endowed with a distributive lattice structure having some combinatorial relevance. Finally we prove that our lattices are isomorphic to the posets of 312- avoiding permutations with the order induced by the strong Bruhat order of the symmetric group.
2005
22
311
328
E. BARCUCCI; A. BERNINI; L. FERRARI; M. PONETI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/250458
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