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no. 5
Birational rowmotion and the octahedron recurrence
Johnson, Joseph1; Liu, Ricky Ini2
1 KTH Royal Institute of Technology Department of Mathematics Stockholm 114 28 (Sweden)
2 University of Washington Department of Mathematics Seattle WA 98195 (USA)
Algebraic Combinatorics, Volume 7 (2024) no. 5, pp. 1453-1477.

We use the octahedron recurrence to give a simplified statement and proof of a formula for iterated birational rowmotion on a product of two chains, first described by Musiker and Roby. Using this, we show that weights of certain chains in rectangles shift in a predictable way under the action of rowmotion. We then define generalized Stanley–Thomas words whose cyclic rotation uniquely determines birational rowmotion on the product of two chains. We also discuss the relationship between rowmotion and birational RSK and give a birational analogue of Greene’s theorem in this setting.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.385
Classification: 05E18, 05A05
Keywords: rowmotion, RSK correspondence, octahedron recurrence, Stanley–Thomas words

Johnson, Joseph 1; Liu, Ricky Ini 2

1 KTH Royal Institute of Technology Department of Mathematics Stockholm 114 28 (Sweden)
2 University of Washington Department of Mathematics Seattle WA 98195 (USA)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Johnson, Joseph; Liu, Ricky Ini. Birational rowmotion and the octahedron recurrence. Algebraic Combinatorics, Volume 7 (2024) no. 5, pp. 1453-1477. doi : 10.5802/alco.385. https://alco.centre-mersenne.org/articles/10.5802/alco.385/

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