| 1. |
- Aas, Erik, et al.
(författare)
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Limiting directions for random walks in classical affine Weyl groups
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Let be a finite Weyl group and the corresponding affine Weyl group. A random element of can be obtained as a reduced random walk on the alcoves of . By a theorem of Lam (Ann. Probab. 2015), such a walk almost surely approaches one of many directions. We compute these directions when is , and and the random walk is weighted by Kac and dual Kac labels. This settles Lam's questions for types and in the affirmative and for type in the negative. The main tool is a combinatorial two row model for a totally asymmetric simple exclusion process called the -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
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Annan publikation (övrigt vetenskapligt/konstnärligt)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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| 3. |
- Linusson, Svante, et al.
(författare)
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On random shifted standard Young tableaux and 132-avoiding sorting networks
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We study shifted standard Young tableaux (SYT). The limiting surface of uniformly random shifted SYT of staircase shape is determined, with the integers in the SYT as heights. This implies via properties of the Edelman-Greene bijection results about random 132-avoiding sorting networks, including limit shapes for trajectories and intermediate permutations. Moreover, the expected number of adjacencies in SYT is considered. It is shown that on average each row and each column of a shifted SYT of staircase shape contains precisely one adjacency.
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| 4. |
- Linusson, Svante, et al.
(författare)
-
On random shifted standard Young tableaux and 132-avoiding sorting networks
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We study shifted standard Young tableaux (SYT). The limiting surface of uniformly random shifted SYT of staircase shape is determined, with the integers in the SYT as heights. This implies via properties of the Edelman-Greene bijection results about random 132-avoiding sorting networks, including limit shapes for trajectories and intermediate permutations. Moreover, the expected number of adjacencies in SYT is considered. It is shown that on average each row and each column of a shifted SYT of staircase shape contains precisely one adjacency.
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| 5. |
- Linusson, Svante, et al.
(författare)
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On random shifted standard Young tableaux and 132-avoiding sorting networks
- 2020
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Ingår i: Algebraic Combinatorics. - : Cellule MathDoc/CEDRAM. - 2589-5486. ; 3:6, s. 1231-1258
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Tidskriftsartikel (refereegranskat)abstract
- We study shifted standard Young tableaux (SYT). The limiting surface of uniformly random shifted SYT of staircase shape is determined, with the integers in the SYT as heights. This implies via properties of the Edelman-Greene bijection results about random 132-avoiding sorting networks, including limit shapes for trajectories and intermediate permutations. Moreover, the expected number of adjacencies in SYT is considered. It is shown that on average each row and each column of a shifted SYT of staircase shape contains precisely one adjacency.
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| 6. |
- 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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| 7. |
- Linusson, Svante, et al.
(författare)
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New properties of the Edelman-Greene bijection
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Edelman and Greene constructed a correspondence between reduced words of the reverse permutation and standard Young tableaux. We prove that for any reduced word the shape of the region of the insertion tableau containing the smallest possible entries evolves exactly as the upper-left component of the permutation's (Rothe) diagram. Properties of the Edelman-Greene bijection restricted to 132-avoiding and 2143-avoiding permutations are presented. We also consider the Edelman-Greene bijection applied to non-reduced words.
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| 8. |
- Linusson, Svante, et al.
(författare)
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On random shifted standard Young tableaux and 132-avoiding sorting networks
- 2019
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Ingår i: FPSAC 2019 - 31st International Conference on Formal Power Series and Algebraic Combinatorics. - : Formal Power Series and Algebraic Combinatorics. ; :82
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Konferensbidrag (refereegranskat)abstract
- We study shifted standard Young tableaux (SYT). The limiting surface of uniformly random shifted SYT of staircase shape is determined, with the integers in the SYT as heights. This implies via properties of the Edelman-Greene bijection results about random 132-avoiding sorting networks, including limit shapes for trajectories and intermediate permutations. Moreover, the expected number of adjacencies in SYT is considered. It is shown that on average each row and each column of a shifted SYT of staircase shape contains precisely one adjacency.
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| 9. |
- Linusson, Svante, et al.
(författare)
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Properties of the Edelman-Greene bijection
- 2020
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Ingår i: Journal of Combinatorics. - Somerville, MA. - 2156-3527 .- 2150-959X. ; 11:2, s. 249-273
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Tidskriftsartikel (refereegranskat)abstract
- Edelman and Greene constructed a bijective correspondence between reduced words of the reverse permutation and standard Young tableaux. We prove that for any reduced word the shape of the region of the insertion tableau containing the smallest possible entries evolves exactly as the upper-left component of the permutation's (Rothe) diagram. Properties of the Edelman-Greene bijection restricted to 132-avoiding and 2143-avoiding permutations are presented. We also consider the Edelman-Greene bijection applied to non-reduced words.
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| 10. |
- Potka, Samu, 1991-
(författare)
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Limit shapes of standard Young tableaux and sorting networks via the Edelman-Greene correspondence
- 2018
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of the following two articles.New properties of the Edelman–Greene bijection. Edelman and Greene constructed a correspondence between reduced words of the reverse permutation and standard Young tableaux. We prove that for any reduced word the shape of the region of the insertion tableau containing the smallest possible entries evolves exactly as the upper-left component of the permutation’s (Rothe) diagram. Properties of the Edelman–Greene bijection restricted to 132-avoiding and 2143-avoiding permutations are presented. We also consider the Edelman-Greene bijection applied to non-reduced words.On random shifted standard Young tableaux and 132-avoiding sorting networks. We study shifted standard Young tableaux (SYT). The limiting surface of uniformly random shifted SYT of staircase shape is determined, with the integers in the SYT as heights. This implies via properties of the Edelman–Greene bijection results about random 132-avoiding sorting networks, including limit shapes for trajectories and intermediate permutations. Moreover, the expected number of adjacencies in SYT is considered. It is shown that on average each row and each column of a shifted SYT of staircase shape contains precisely one adjacency.
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