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R-systems
Name
29_2019_470_ReferencePDF.pdf
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574.99 KB
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Adobe PDF
Checksum (MD5)
983f15c816065e4590d7e14f3d5c72c5
Author(s)
Galashin, Pavel
Pylyavskyy, Pavlo
Date Issued
March 13, 2019
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.
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DOI of Published Version
https://doi.org/10.1007/s00029-019-0470-2
