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  1. Home > Articles & Issues >
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  3. $Y$ -meshes and gene ...
Conference paper

$Y$ -meshes and generalized pentagram maps

Max Glick (1), Pavlo Pylyavskyy ORCID (1)
(1) School of Mathematics
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Imported on
November 21, 2016
Published on
December 31, 2014
Last modified on
March 31, 2025
Volume
DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Proceedings
DOI
10.46298/dmtcs.2520
License
Attribution 4.0 International (CC BY 4.0)
Some questions in total positivity and cluster algebras
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$Y$ -meshes and generalized pentagram maps

Max Glick (1), Pavlo Pylyavskyy ORCID (1)
(1) School of Mathematics
Abstract
English
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.
French
Nous introduisons une famille de généralisations de l’application pentagramme. Chacune produit une configuration infinie de points et de lignes avec quatre points sur chaque ligne. Ces systèmes ont une description des $Y$ -mutations dans une algèbre amassée, un nouveau lien entre la théorie d’algèbres amassées et la géométrie projective.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • pentagram map
  • discrete dynamical systems
  • cluster algebras
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