Building Irreducible Representations of a Symmetric Group S(n) with Large and Maximum Dimensions
Abstract
Introduction: In combinatorics, Young diagrams and Young tableaux are important mathematical objects. Asymptotic combinatorics studies the asymptotic behaviour of parameters of combinatorial objects. Young diagrams parameterize irreducible representations of a symmetric group. Therefore, the combinatorics of Young diagrams is closely related to asymptotic rep re sentation theory which studies the asymptotic properties of parameters of irreducible representations for classical groups. In 1981, A. M.Vershik posed a problem about the convergence of normalized maximal dimensions of Young diagrams. This problem still remains open. Purpose: Building a sequence of diagrams of large and maximum dimensions which would correspond to irreducible representations of a symmetric group. Methods: We propose a modification of the greedy algorithm which builds a sequence of diagrams with large dimensions. The idea is to enhance the diagram on each level of the graded Young graph. Results: With the proposed algorithm, you can obtain all the maximum dimension diagrams known for today, and also improve some of the existing estimations for the maximum dimensions of Young diagrams for the cases when their exact values are unknown.Published
2015-06-01
How to Cite
Vasilyev, N., & Duzhin, V. (2015). Building Irreducible Representations of a Symmetric Group S(n) with Large and Maximum Dimensions. Information and Control Systems, (3), 17-22. https://doi.org/10.15217/issn1684-8853.2015.3.17
Issue
Section
Theoretical and applied mathematics