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2010

Hall-Littlewood polynomials and fixed point enumeration

13 years 11 months ago
Hall-Littlewood polynomials and fixed point enumeration
We resolve affirmatively some conjectures of Reiner, Stanton, and White [6] regarding enumeration of various classes of matrices which are invariant under certain cyclic row and column rotations. Our results are phrased in terms of the bicyclic sieving phenomenon introduced by Barcelo, Reiner, and Stanton [1]. The proofs of our results use various tools from symmetric function theory such as the Stanton-White rim hook correspondence [9] and results concerning the specialization of Hall-Littlewood polynomials due to Lascoux, Leclerc, and Thibon [2] [3].
Brendon Rhoades
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2010
Where DM
Authors Brendon Rhoades
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