2021/02/19 by Oh, Jaeseong
#05E05 #05E10 #05E18 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2102.09982
The Garsia--Haiman module is a bigraded \mathfrakSn-module whose Frobenius image is a Macdonald polynomial. The method of orbit harmonics promotes an \mathfrakSn-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.