A formula for birational rowmotion on rectangles

Gregg Musiker; Tom Roby

A formula for birational rowmotion on rectangles

Research output: Contribution to conference › Paper › peer-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 language	English (US)
State	Published - 2018
Externally published	Yes
Event	30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 - Hanover, United States Duration: Jul 16 2018 → Jul 20 2018

Conference

Conference	30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018
Country/Territory	United States
City	Hanover
Period	7/16/18 → 7/20/18

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.

Keywords

Birational rowmotion
Dynamical algebraic combinatorics
Periodicity

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N2 - 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].

AB - 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].

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KW - Dynamical algebraic combinatorics

KW - Periodicity

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ER -

A formula for birational rowmotion on rectangles

Abstract

Conference

Bibliographical note

Keywords

OpenUrl availability

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