Geodesic
$Y$ -meshes and generalized pentagram maps
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015).

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We introduce a rich family of generalizations of the pentagram map sharing the property that each generates an infinite configuration of points and lines with four points on each line. These systems all have a description as $Y$ -mutations in a cluster algebra and hence establish new connections between cluster theory and projective geometry. 
@article{DMTCS_2015_special_285_a64,
     author = {Glick, Max and Pylyavskyy, Pavlo},
     title = {$Y$ -meshes and generalized pentagram maps},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)},
     year = {2015},
     doi = {10.46298/dmtcs.2520},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2520/}
}
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%V DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
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Glick, Max; Pylyavskyy, Pavlo. $Y$ -meshes and generalized pentagram maps. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi : 10.46298/dmtcs.2520. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2520/

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