Abstract
Robinson-Schensted-Knuth (RSK) correspondence occurs in different contexts of algebra and combinatorics. Recently, this topic has been actively investigated by many researchers. At the same time, many investigations require conducting the computer experiments involving very large Young tableaux. The article is devoted to such experiments. RSK algorithm establishes a bijection between sequences of elements of linearly ordered set and the pairs of Young tableaux of the same shape called insertion tableau and recording tableau . In this paper we study the dynamics of tableau and the dynamics of different concrete values in tableau during the iterations of RSK algorithm. Particularly, we examine the paths within tableaux called bumping routes along which the elements of an input sequence pass. The results of computer experiments with Young tableaux of sizes up to 108 were presented. These experiments were made using the software package for dealing with 2D and 3D Young diagrams and tableaux.
Highlights
Robinson–Schensted–Knuth (RSK) algorithm known as Robinson– Schensted–Knuth correspondence which maps permutations to the pairs of Young tableaux, plays an important role into various combinatorial problems
In order to study the properties of the RSK algorithm, it is of interest to examine how the shape of tableau P changes in time
The results of numerical experiments presented in this article demonstrate two types of dynamics in an insertion tableau of the Robinson– Schensted–Knuth algorithm
Summary
Robinson–Schensted–Knuth (RSK) algorithm known as Robinson– Schensted–Knuth correspondence which maps permutations to the pairs of Young tableaux, plays an important role into various combinatorial problems. RSK correspondence can be generalized from the case of permutations to the case of infinite sequences of linearly ordered set. In such instance, an insertion tableau is a semi-standard Young tableau filled by elements of this. This implies that the RSK algorithm is applicable to a sequence of random independent values uniformly distributed over the interval [0,1], i.e. to the Bernoulli scheme. It was proved there that the first element of an infinite sequence of uniformly distributed random values can be unambiguously restored only by the limit angle of inclination of Schützenberger path of a recording tableau. The subject of this article is to examine how tableau P changes during RSK insertions
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