A formula for birational rowmotion on rectangles

Gregg Musiker, Tom Roby

Research output: Contribution to conferencePaperpeer-review

Abstract

We give a formula in terms of families of non-intersecting lattice paths for iterated actions of the birational rowmotion map on a product of two chains, equivalently a rectangle. This allows us to give a much simpler direct proof of the key fact that the period of this map on a product of chains of lengths r and s is r + s + 2 (first proved by D. Grinberg and the second author) as well as other consequences, as explained in [8].

Original languageEnglish (US)
StatePublished - 2018
Event30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 - Hanover, United States
Duration: Jul 16 2018Jul 20 2018

Conference

Conference30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018
Country/TerritoryUnited States
CityHanover
Period7/16/187/20/18

Bibliographical note

Funding Information:
∗musiker@math.umn.edu. Partially supported by NSF Grant DMS-1362980. †tom.roby@uconn.edu

Publisher Copyright:
© FPSAC 2018 - 30th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

Keywords

  • Birational rowmotion
  • Dynamical algebraic combinatorics
  • Periodicity

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