Open AccessSearch for Young diagrams with large dimensions
Author(s) -
Vasilii Duzhin,
Anastasia A. Chudnovskaya
Publication year - 2019
Publication title -
kompʹûternye instrumenty v obrazovanii
Language(s) - English
Resource type - Journals
eISSN - 2071-2359
pISSN - 2071-2340
DOI - 10.32603/2071-2340-2019-4-33-43
Subject(s) - dimension (graph theory) , sequence (biology) , diagram , mathematics , combinatorics , young tableau , statistics , genetics , biology
Search for Young diagrams with maximum dimensions or, equivalently, search for irreducible representations of the symmetric group $S(n)$ with maximum dimensions is an important problem of asymptotic combinatorics. In this paper, we propose algorithms that transform a Young diagram into another one of the same size but with a larger dimension. As a result of massive numerical experiments, the sequence of $10^6$ Young diagrams with large dimensions was constructed. Furthermore, the proposed algorithms do not change the first 1000 elements of this sequence. This may indicate that most of them have the maximum dimension. It has been found that the dimensions of all Young diagrams of the resulting sequence starting from the 75778th exceed the dimensions of corresponding diagrams of the greedy Plancherel sequence.