Random strict partitions and random shifted tableaux

Matsumoto, Sho; Śniady, Piotr

doi:10.1007/s00029-020-0535-2

Cited by 6 publications

(2 citation statements)

References 40 publications

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“…n  As in many problems of asymptotic combinatorics, such experiments require the involvement of a huge number of large Young tableaux. A similar problem and the RSK algorithm itself, are also defined for the case of strict Young tableaux and the Plancherel process on the Schur graph [15][16][17]. These two Plancherel processes have a close relationship.…”

Section: Discussionmentioning

confidence: 99%

Modeling of bumping routes in the RSK algorithm and analysis of their approach to limit shapes

Vassiliev

Duzhin

Kuzmin

2022

ICS

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Introduction: The RSK algorithm establishes an equivalence of finite sequences of elements of linearly ordered sets and pairs of Young tableaux P and Q of the same shape. Of particular interest is the study of the asymptotic limit, i. e., the limit shape of the so-called bumping routes formed by the boxes of tableau P affected in a single iteration of the RSK algorithm. The exact formulae for these limit shapes were obtained by D. Romik and P. Śniady in 2016. However, the problem of investigating the dynamics of the approach of bumping routes to their limit shapes remains insufficiently studied. Purpose: To study the dynamics of distances between the bumping routes and their limit shapes in Young tableaux with the help of computer experiments. Results: We have obtained a large number of experimental bumping routes through a series of computer experiments for Young tableaux P of sizes up to 4·106, filled with real numbers in the range [0, 1] and sets of inserted values α Î [0.1, 0.15, … , 0.85]. We have compared these bumping routes in the L2 metric with the corresponding limit shapes and have calculated the average distances and variances of their deviations from the limit shapes. We present an empirical formula for the rate of approach of discretized bumping routes to their limit shapes. Also, the experimental parameters of the normal distributions of the deviations of the bumping routes are obtained for various input values.

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Section: Discussionmentioning

confidence: 99%

Modeling of bumping routes in the RSK algorithm and analysis of their approach to limit shapes

Vassiliev

Duzhin

Kuzmin

2022

ICS

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“…However, it was pointed out to us by one of the referees that Biane [2] provides a general method for computing such limits for SYT. Recently, Matsumoto and Śniady developed an analogous framework for shifted SYT which, combined with the results of [2] and [27], allowed them to partially recover Theorem 3.7 in [22,Sec. 8.4].…”

Section: Introductionmentioning

confidence: 99%

On random shifted standard Young tableaux and 132-avoiding sorting networks

Linusson¹,

Potka²,

Sulzgruber³

2020

Algebraic Combinatorics

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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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