Using the notion of series parallel interval order, we propose a unified setting to describe Dyck lattices and Tamari lattices (two well known lattice structures on Catalan objects) in terms of basic notions of the theory of posets. As a consequence of our approach, we find an extremely simple proof of the fact that the Dyck order is a refinement of the Tamari one. Moreover, we provide a description of both the weak and the strong Bruhat order on 312-avoiding permutations, by recovering the proof of the fact that they are isomorphic to the Tamari and the Dyck order, respectively; our proof, which simplifies the existing ones, relies on our results on series parallel interval orders.

Disanto, F., Ferrari, L., Pinzani, P., Rinaldi, S. (2012). Catalan lattices on series parallel interval orders. In Associahedra, Tamari lattices, and Related Structures (Tamari Mamorial Festschrift) (pp. 323-338). Berlin : Springer [10.1007/978-3-0348-0405-9_16].

Catalan lattices on series parallel interval orders

RINALDI, SIMONE
2012-01-01

Abstract

Using the notion of series parallel interval order, we propose a unified setting to describe Dyck lattices and Tamari lattices (two well known lattice structures on Catalan objects) in terms of basic notions of the theory of posets. As a consequence of our approach, we find an extremely simple proof of the fact that the Dyck order is a refinement of the Tamari one. Moreover, we provide a description of both the weak and the strong Bruhat order on 312-avoiding permutations, by recovering the proof of the fact that they are isomorphic to the Tamari and the Dyck order, respectively; our proof, which simplifies the existing ones, relies on our results on series parallel interval orders.
9783034804042
978-3-0348-0405-9
Disanto, F., Ferrari, L., Pinzani, P., Rinaldi, S. (2012). Catalan lattices on series parallel interval orders. In Associahedra, Tamari lattices, and Related Structures (Tamari Mamorial Festschrift) (pp. 323-338). Berlin : Springer [10.1007/978-3-0348-0405-9_16].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/23253
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