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Double Catalan monoids
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
2012 (English)In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 36, no 3, 333-354 p.Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
2012. Vol. 36, no 3, 333-354 p.
Keyword [en]
Catalan monoid, Presentation, Pattern avoiding permutation, Effective representation
National Category
URN: urn:nbn:se:uu:diva-182737DOI: 10.1007/s10801-011-0336-yISI: 000308700600001OAI: oai:DiVA.org:uu-182737DiVA: diva2:561615
Available from: 2012-10-19 Created: 2012-10-15 Last updated: 2012-10-19Bibliographically approved

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Mazorchuk, Volodymyr
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Algebra and Geometry
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