Geodesic
Birational rowmotion and Coxeter-motion on minuscule posets
Soichi Okada1
1Nagoya University
The electronic journal of combinatorics, Tome 28 (2021) no. 1
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Birational rowmotion is a discrete dynamical system on the set of all positive real-valued functions on a finite poset, which is a birational lift of combinatorial rowmotion on order ideals. It is known that combinatorial rowmotion for a minuscule poset has order equal to the Coxeter number, and exhibits the file homomesy phenomenon for refined order ideal cardinality statistics. In this paper we generalize these results to the birational setting. Moreover, as a generalization of birational promotion on a product of two chains, we introduce birational Coxeter-motion on minuscule posets, and prove that it enjoys periodicity and file homomesy.
DOI : 10.37236/9557
Classification : 05E18, 06A11
Mots-clés : birational Coxeter-motion on minuscule posets

Soichi Okada  1

1 Nagoya University 
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     author = {Soichi Okada},
     title = {Birational rowmotion and {Coxeter-motion} on minuscule posets},
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     year = {2021},
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Soichi Okada. Birational rowmotion and Coxeter-motion on minuscule posets. The electronic journal of combinatorics, Tome 28 (2021) no. 1. doi: 10.37236/9557

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