Papers by Nikolay Vassiliev
The Robinson-Schensted-Knuth (RSK) correspondence is a bijection between a set of permutations of... more The Robinson-Schensted-Knuth (RSK) correspondence is a bijection between a set of permutations of integers and a set of pairs of Young tableaux of the same shape: insertion tableaux P and recording tableaux Q. The procedure of transforming the input permutation into tableaux is also known as the RSK algorithm or the RSK transformation. The RSK algorithm has many important applications in combinatorics and representation theory. Each number from the input permutation is being put into a certain place of tableau P , consequently displacing other numbers when it is necessary. A bumping route [1] is a sequence of positions in insertion tableau where bumping occures during the RSK transformation. At the same time, tableau Q "records" the position where the form of P has changed by putting the index of the current number at the same position. A more detailed description of the RSK algorithm can be found in [2]. The RSK algorithm can be easily generalized to the infinite case: th...
Information and Control Systems, 2021
Introduction: The Robinson — Schensted — Knuth (RSK) algorithm transforms a sequence of elements ... more Introduction: The Robinson — Schensted — Knuth (RSK) algorithm transforms a sequence of elements of a linearly ordered set into a pair of Young tableaux P, Q of the same shape. This transformation is based on the process of bumping and inserting elements in tableau P according to special rules. The trajectory formed by all the boxes of the tableau P shifted in the RSK algorithm is called the bumping route. D. Romik and P. Śniady in 2016 obtained an explicit formula for the limit shape of the bumping route, which is determined by its first element. However, the rate of convergence of the bumping routes to the limit shape has not been previously investigated either theoretically or by numerical experiments. Purpose: Carrying out computer experiments to study the dynamics of the bumping routes produced by the RSK algorithm on Young tableaux as their sizes increase. Calculation of statistical means and variances of deviations of bumping routes from their limit shapes in the L2 metric fo...
Journal of Mathematical Sciences, 2020
There exists a well-known hook-length formula for calculating the dimensions of 2D Young diagrams... more There exists a well-known hook-length formula for calculating the dimensions of 2D Young diagrams. Unfortunately, the analogous formula for 3D case is unknown. We introduce an approach for calculating the estimations of dimensions of three-dimensional Young diagrams also known as plane partitions. The most difficult part of this task is the calculation of co-transition probabilities. We propose to approximately calculate these probabilities by generating numerous random paths to a given diagram. In case the generated paths are uniformly distributed, the proportion of paths passing through a certain branch gives us the co-transition probability. As our numerical experiments show, the random generator based on the Schützenberger transformation, gives the distribution of Young tableaux close to uniform.
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Papers by Nikolay Vassiliev