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- W4285385873 abstract "In 2015, Brosnan and Chow, and independently Guay-Paquet, proved the Shareshian-Wachs conjecture, which links the Stanley-Stembridge conjecture in combinatorics to the geometry of Hessenberg varieties through Tymoczko's permutation group action on the cohomology ring of regular semisimple Hessenberg varieties. In previous work, the authors exploited this connection to prove a graded version of the Stanley-Stembridge conjecture in a special case. In this manuscript, we derive a new set of linear relations satisfied by the multiplicities of certain permutation representations in Tymoczko's representation. We also show that these relations are upper-triangular in an appropriate sense, and in particular, they uniquely determine the multiplicities. As an application of these results, we prove an inductive formula for the multiplicity coefficients corresponding to partitions with a maximal number of parts." @default.
- W4285385873 created "2022-07-14" @default.
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- W4285385873 date "2022-07-15" @default.
- W4285385873 modified "2023-10-14" @default.
- W4285385873 title "Upper Triangular Linear Relations on Mmultiplicities and the Stanley-Stembridge Conjecture" @default.
- W4285385873 doi "https://doi.org/10.37236/10489" @default.
- W4285385873 hasPublicationYear "2022" @default.
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