| 1. |
- Alexandersson, Per, 1987-, et al.
(author)
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Promotion and cyclic sieving on families of SSYT
- 2021
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In: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 59:2, s. 247-274
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Journal article (peer-reviewed)abstract
- We examine a few families of semistandard Young tableaux, for which we observe the cyclic sieving phenomenon under promotion. The first family we consider consists of stretched hook shapes, where we use the cocharge generating polynomial as CSP-polynomial. The second family contains skew shapes, consisting of disjoint rectangles. Again, the charge generating polynomial together with promotion exhibits the cyclic sieving phenomenon. This generalizes earlier results by B. Rhoades and later B. Fontaine and J. Kamnitzer. Finally, we consider certain skew ribbons, where promotion behaves in a predictable manner. This result is stated in the form of a bicyclic sieving phenomenon. One of the tools we use is a novel method for computing charge of skew semistandard tableaux, in the case when every number in the tableau occurs with the same frequency.
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| 2. |
- Alexandersson, Per, et al.
(author)
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Refined Catalan and Narayana cyclic sieving
- 2021
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In: Combinatorial Theory. - : California Digital Library (CDL). - 2766-1334. ; 1:0
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Journal article (peer-reviewed)abstract
- We prove several new instances of the cyclic sieving phenomenon (CSP) on Catalan objects of type A and type B . Moreover, we refine many of the known instances of the CSP on Catalan objects. For example, we consider triangulations refined by the number of "ears", non-crossing matchings with a fixed number of short edges, and non-crossing configurations with a fixed number of loops and edges.
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