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Spring 2010 $SL_k$-tilings of the plane
François Bergeron, Christophe Reutenauer
Illinois J. Math. 54(1): 263-300 (Spring 2010). DOI: 10.1215/ijm/1299679749

Abstract

We study properties of (bi-infinite) arrays having all adjacent $k\times k$ adjacent minors equal to one. If we further add the condition that all adjacent $(k-1)\times(k-1)$ minors be nonzero, then these arrays are necessarily of rank $k$. It follows that we can explicit construct all of them. Several nice properties are made apparent. In particular, we revisit, with this perspective, the notion of frieze patterns of Coxeter. This shed new light on their properties. A connexion is also established with the notion of $T$-systems of Statistical Physics.

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François Bergeron. Christophe Reutenauer. "$SL_k$-tilings of the plane." Illinois J. Math. 54 (1) 263 - 300, Spring 2010. https://doi.org/10.1215/ijm/1299679749

Information

Published: Spring 2010
First available in Project Euclid: 9 March 2011

zbMATH: 1236.13018
MathSciNet: MR2776996
Digital Object Identifier: 10.1215/ijm/1299679749

Subjects:
Primary: 15A15
Secondary: 05A05, 05E10, 11C20

Rights: Copyright © 2010 University of Illinois at Urbana-Champaign

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Vol.54 • No. 1 • Spring 2010
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