A software package for studying problems of asymptotic combinatorics of Young diagrams and Young tableaux
Keywords:
Young diagrams, Young tableaux, Robinson-Schensted-Knuth algorithm, RSK correspondence, jeu de taquin, asymptotic combinatoricsAbstract
Introduction: It is often impossible to solve fundamental problems of asymptotic combinatorics without conducting massive computer experiments. However, carrying out such experiments usually requires significant computational costs. In this regard, the task of developing effective software tools is relevant. Purpose: To develop a software package for working with Young diagrams and Young tableaux. Results: A software package has been implemented in C++ which makes it possible to work with two- and three-dimensional Young diagrams and Young tableaux, as well as model various Markov processes on graded graphs. Numerous operations on Young tableaux have been implemented, including the Robinson-Schensted-Knuth algorithm and the Schützenberger’s jeu de taquin. The software tools also include rich functionality for visualizing various combinatorial objects. Practical relevance: The software package is written in C++, which gives an advantage over traditional approaches using computer algebra systems in terms of efficiency, with the specifics of many problems of asymptotic combinatorics taken into account. The developed software package was used to conduct numerous computer experiments in the process of modeling the dynamics of the behaviour of various objects of asymptotic combinatorics. The modeling results have formed the basis for a number of scientific publications.