Séminaire Lotharingien de Combinatoire, 80B.37 (2018), 12 pp.
Gregg Musiker and Tom Roby
A Formula for Birational Rowmotion on Rectangles
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].
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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