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TITLE Macdonald polynomials and cyclic sieving
KIAS AUTHORS Oh, Jaeseong
JOURNAL EUROPEAN JOURNAL OF COMBINATORICS, 2022
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ABSTRACT The Garsia-Haiman module is a bigraded en-module whose Frobenius image is a Macdonald polynomial. The method of orbit harmonics promotes an en-set X to a graded polynomial ring. The orbit harmonics can be applied to prove cyclic sieving phenomena which is a notion that encapsulates the fixed-point structure of finite cyclic group action on a finite set. By applying this idea to the Garsia-Haiman module, we provide cyclic sieving results regarding the enumeration of matrices that are invariant under certain cyclic row and column rotation and translation of entries. (C) 2021 Elsevier Ltd. All rights reserved.
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