The pentagram map and Y-patterns

International audience The pentagram map, introduced by R. Schwartz, is defined by the following construction: given a polygon as input, draw all of its ``shortest'' diagonals, and output the smaller polygon which they cut out. We employ the machinery of cluster algebras to obtain explicit...

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Bibliographic Details
Main Author: Glick, Max
Other Authors: Department of Mathematics - University of Michigan, University of Michigan Ann Arbor, University of Michigan System-University of Michigan System, Bousquet-Mélou, Mireille and Wachs, Michelle and Hultman, Axel
Format: Conference Object
Language:English
Published: HAL CCSD 2011
Subjects:
pentagram map
cluster algebra
Y-pattern
alternating sign matrix
[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Iceland
Online Access:https://hal.inria.fr/hal-01215101
https://hal.inria.fr/hal-01215101/document
https://hal.inria.fr/hal-01215101/file/dmAO0136.pdf
Description
Summary:International audience The pentagram map, introduced by R. Schwartz, is defined by the following construction: given a polygon as input, draw all of its ``shortest'' diagonals, and output the smaller polygon which they cut out. We employ the machinery of cluster algebras to obtain explicit formulas for the iterates of the pentagram map. L'application pentagramme de R. Schwartz est définie par la construction suivante: on trace les diagonales ``les plus courtes'' d'un polygone donné en entrée et on retourne en sortie le plus petit polygone que ces diagonales découpent. Nous employons la machinerie des algèbres ``clusters'' pour obtenir des formules explicites pour les itérations de l'application pentagramme.

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