Dihedral Sieving Phenomena
نویسنده
چکیده
Abstract. Cyclic sieving is a well-known phenomenon where certain interesting polynomials, especially qanalogues, have useful interpretations related to actions and representations of the cyclic group. We define sieving for an arbitrary group G and study it for the dihedral group I2pnq of order 2n. This requires understanding the generators of the representation ring of the dihedral group. For n odd, we exhibit several instances of “dihedral sieving” which involve the generalized Fibonomial coefficients, recently studied by Sagan et al.. In addition, we give some recursively-defined polynomials which may help prove instances of dihedral sieving for even n.
منابع مشابه
Cyclic sieving, promotion, and representation theory
We prove a collection of conjectures of D. White [37], as well as some related conjectures of Abuzzahab-Korson-Li-Meyer [1] and of Reiner and White [21], [37], regarding the cyclic sieving phenomenon of Reiner, Stanton, and White [22] as it applies to jeu-de-taquin promotion on rectangular tableaux. To do this, we use Kazhdan-Lusztig theory and a characterization of the dual canonical basis of ...
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