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Double Catalan monoids
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
2012 (engelsk)Inngår i: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 36, nr 3, s. 333-354Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In this paper, we define and study what we call the double Catalan monoid. This monoid is the image of a natural map from the 0-Hecke monoid to the monoid of binary relations. We show that the double Catalan monoid provides an algebraization of the (combinatorial) set of 4321-avoiding permutations and relate its combinatorics to various off-shoots of both the combinatorics of Catalan numbers and the combinatorics of permutations. In particular, we give an algebraic interpretation of the first derivative of the Kreweras involution on Dyck paths, of 4321-avoiding involutions and of recent results of Barnabei et al. on admissible pairs of Dyck paths. We compute a presentation and determine the minimal dimension of an effective representation for the double Catalan monoid. We also determine the minimal dimension of an effective representation for the 0-Hecke monoid.

sted, utgiver, år, opplag, sider
2012. Vol. 36, nr 3, s. 333-354
Emneord [en]
Catalan monoid, Presentation, Pattern avoiding permutation, Effective representation
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Identifikatorer
URN: urn:nbn:se:uu:diva-182737DOI: 10.1007/s10801-011-0336-yISI: 000308700600001OAI: oai:DiVA.org:uu-182737DiVA, id: diva2:561615
Tilgjengelig fra: 2012-10-19 Laget: 2012-10-15 Sist oppdatert: 2017-12-07bibliografisk kontrollert

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