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Higher pentagram maps, weighted directed networks, and cluster dynamics
 Electron.Res.Announc.Math.Sci.19
"... cluster dynamics ..."
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Discrete integrable systems and Poisson algebras from cluster maps, arXiv: 1207.6072v2
, 2012
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Arithmetics of 2friezes
 J. Algebraic Combin
"... Abstract. We consider the variant of CoxeterConway frieze patterns called 2frieze. We prove that there exist infinitely many closed integral 2friezes (i.e. containing only positive integers) provided the width of the array is bigger than 4. We introduce operations on the integral 2friezes genera ..."
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Abstract. We consider the variant of CoxeterConway frieze patterns called 2frieze. We prove that there exist infinitely many closed integral 2friezes (i.e. containing only positive integers) provided the width of the array is bigger than 4. We introduce operations on the integral 2friezes generating bigger or smaller closed integral 2friezes. 1.
Cyclic Sieving of Increasing Tableaux and Small Schröder Paths
, 2013
"... An increasing tableau is a semistandard tableau with strictly increasing rows and columns. It is well known that the Catalan numbers enumerate both rectangular standard Young tableaux of two rows and also Dyck paths. We generalize this to a bijection between rectangular 2row increasing tableaux an ..."
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An increasing tableau is a semistandard tableau with strictly increasing rows and columns. It is well known that the Catalan numbers enumerate both rectangular standard Young tableaux of two rows and also Dyck paths. We generalize this to a bijection between rectangular 2row increasing tableaux and small Schröder paths. Using the jeu de taquin for increasing tableaux of [Thomas–Yong ’09], we then present a new instance of the cyclic sieving phenomenon of [Reiner–Stanton–White ’04].
SL2(Z)tiling of the torus, CoxeterConway friezes and Farey triangulations
, 2014
"... The notion of SL2tiling is a generalization of that of classical CoxeterConway frieze pattern. We classify doubly antiperiodic SL2tilings that contain a rectangular domain of positive integers. Every such SL2tiling corresponds to a pair of frieze patterns and a unimodular 2 × 2matrix with posi ..."
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The notion of SL2tiling is a generalization of that of classical CoxeterConway frieze pattern. We classify doubly antiperiodic SL2tilings that contain a rectangular domain of positive integers. Every such SL2tiling corresponds to a pair of frieze patterns and a unimodular 2 × 2matrix with positive integer coefficients. We relate this notion to triangulated ngons in the Farey graph.