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SL₂-tilings and triangulations of the strip

Lookup NU author(s): Professor Peter Jorgensen

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Abstract

SL2-tilings were introduced by Assem, Reutenauer, and Smith in connection with frieses and their applications to cluster algebras. An SL2-tiling is a bi-infinite matrix of positive integers such that each adjacent 2 x 2-submatrix has determinant 1. In this paper we define the class of SL2-tilings with enough ones. It contains the previously known tilings as well as some which are new, and we show that it is in bijection with a certain class of combinatorial objects, namely "good" triangulations of the strip. (C) 2013 Elsevier Inc. All rights reserved.

Publication metadata

Author(s): Holm T, Jorgensen P

Publication type: Article

Publication status: Published

Journal: Journal of Combinatorial Theory, Series A

Year: 2013

Volume: 120

Issue: 7

Pages: 1817-1834

Print publication date: 20/07/2013

ISSN (print): 0097-3165

ISSN (electronic): 1096-0899

Publisher: Academic Press

URL: http://dx.doi.org/10.1016/j.jcta.2013.07.001

DOI: 10.1016/j.jcta.2013.07.001

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