Work

Birational rowmotion and the octahedron recurrence

Year: 2024

Type: article

Abstract: 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.

Source: Algebraic Combinatorics

DOI: 10.5802/alco.385

Authors: Joseph Johnson, Ricky Ini Liu

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Johns Hopkins University

Awards: AF: Medium: Theory of Computation - New Algorithmic and Hardness Techniques, Combinatorics and Geometry of Symmetric Group Representations

OpenAlex ID: W4403940536