R-systems
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Pavel Galashin [1] ; Pavlo Pylyavskyy [2]
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[1] Massachusetts Institute of Technology
Massachusetts Institute of Technology
City of Cambridge, Estados Unidos
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[2] University of Minnesota
University of Minnesota
City of Minneapolis, Estados Unidos
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- Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 2, 2019
- Idioma: inglés
- DOI: 10.1007/s00029-019-0470-2
- Enlaces
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Resumen
Birational toggling on GelfandâTsetlin patterns appeared first in the study of geometric crystals and geometric RobinsonâSchenstedâKnuth 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.
