Moving from a well-known natural order on Dyck paths of any fixed length inducing a distributive lattice, we transfer this order on noncrossing partitions along a famous bijection, 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 on noncrossing partitions / E. BARCUCCI; A. BERNINI; L. FERRARI; M. PONETI. - ELETTRONICO. - (2005), pp. 435-444. (Intervento presentato al convegno FPSAC 2005 tenutosi a Taormina nel 20 - 25 giugno 2005).
A distributive lattice structure on noncrossing partitions
BARCUCCI, ELENA;BERNINI, ANTONIO;FERRARI, LUCA;
2005
Abstract
Moving from a well-known natural order on Dyck paths of any fixed length inducing a distributive lattice, we transfer this order on noncrossing partitions along a famous bijection, 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.
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