| 1. |
- Aas, Erik, et al.
(författare)
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Limiting Directions for Random Walks in Classical Affine Weyl Groups
- 2021
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Ingår i: International mathematics research notices. - : Oxford University Press (OUP). - 1073-7928 .- 1687-0247. ; 2023:4, s. 3092-3137
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Tidskriftsartikel (refereegranskat)abstract
- Let W be a finite Weyl group and (W) over tilde the corresponding affine Weyl group. A random element of (W) over tilde can be obtained as a reduced random walk on the alcoves of (W) over tilde. By a theorem of Lam (Ann. Prob. 2015), such a walk almost surely approaches one of vertical bar W vertical bar many directions. We compute these directions when W is B-n, C-n, and D-n, and the random walk is weighted by Kac and dual Kac labels. This settles Lam's questions for types B and C in the affirmative and for type D in the negative. The main tool is a combinatorial two row model for a totally asymmetric simple exclusion process (TASEP) called the D*-TASEP, with four parameters. By specializing the parameters in different ways, we obtain TASEPs for each of the Weyl groups mentioned above. Computing certain correlations in these TASEPs gives the desired limiting directions.
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| 2. |
- Alexandersson, Per, et al.
(författare)
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Refined Catalan and Narayana cyclic sieving
- 2021
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Ingår i: Combinatorial Theory. - : California Digital Library (CDL). - 2766-1334. ; 1:0
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Tidskriftsartikel (refereegranskat)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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