R-systems
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29_2019_470_ReferencePDF.pdf
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574.99 KB
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983f15c816065e4590d7e14f3d5c72c5
Author(s)
Galashin, Pavel
Pylyavskyy, Pavlo
Date Issued
March 13, 2019
Journal
Selecta Mathematica
Publisher
Springer International Publishing
Citation
Selecta Mathematica. 2019 Mar 13;25(2):22
Version
Author's final manuscript
Abstract
Abstract
Birational toggling on Gelfand–Tsetlin patterns appeared first in the study of geometric crystals and geometric Robinson–Schensted–Knuth correspondence. Based on these birational toggle relations, Einstein and Propp introduced a discrete dynamical system called birational rowmotion associated with a partially ordered set. We generalize birational rowmotion to the class of arbitrary strongly connected directed graphs, calling the resulting discrete dynamical system the R-system. We study its integrability from the points of view of singularity confinement and algebraic entropy. We show that in many cases, singularity confinement in an R-system reduces to the Laurent phenomenon either in a cluster algebra, or in a Laurent phenomenon algebra, or beyond both of those generalities, giving rise to many new sequences with the Laurent property possessing rich groups of symmetries. Some special cases of R-systems reduce to Somos and Gale-Robinson sequences.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00029-019-0470-2
