Statistics of the symmetric group representations as a natural science question on asymptotics of Young diagrams

2011 ◽  
pp. 1-7 ◽  
Author(s):  
Vladimir Arnold
Keyword(s):  
Symmetric Group ◽  
Natural Science ◽  
Young Diagrams ◽  
Group Representations ◽  
Science Question ◽  
Symmetric Group Representations

scholarly journals Symmetric group representations andZ

2018 ◽  
Vol 356 (1) ◽  
pp. 1-4
Author(s):  
Anshul Adve ◽  
Alexander Yong
Keyword(s):  
Symmetric Group ◽  
Group Representations ◽  
Symmetric Group Representations

Products and Plethysms of Characters with Orthogonal, Symplectic and Symmetric Groups

1958 ◽  
Vol 10 ◽  
pp. 17-32 ◽  
Author(s):  
D. E. Littlewood
Keyword(s):  
Symmetric Group ◽  
Kronecker Product ◽  
Symmetric Groups ◽  
Group Representations ◽  
Symmetric Group Representations

Murnaghan (9) has proposed the following method of analyzing the Kronecker product of two symmetric group representations. If (λ) = (λ1, λ2, … , λi) is a partition of p, the representation of the symmetric group on n symbols corresponding to the partition (n — p, λ1 , … , λi) is denoted by [λ] and is said to be of depth p. If [λ] is of depth p and [μ] of depth q, then the terms in the Kronecker product [λ] X [μ] of depth p + q are terms which correspond to the terms in the product of S-functions {λ} {μ}).

scholarly journals On signed Young permutation modules and signed p-Kostka numbers

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Eugenio Giannelli ◽  
Kay Jin Lim ◽  
William O’Donovan ◽  
Mark Wildon
Keyword(s):  
Symmetric Group ◽  
Group Representations ◽  
Kostka Numbers ◽  
Basic Facts ◽  
Symmetric Group Representations

AbstractWe prove the existence and main properties of signed Young modules for the symmetric group, using only basic facts about symmetric group representations and the Broué correspondence. We then prove new reduction theorems for the signed

HOPF ALGEBRAS OF SYMMETRIC FUNCTIONS AND TENSOR PRODUCTS OF SYMMETRIC GROUP REPRESENTATIONS

1991 ◽  
Vol 01 (02) ◽  
pp. 207-221 ◽  
Author(s):  
JEAN-YVES THIBON
Keyword(s):  
Hopf Algebra ◽  
Tensor Product ◽  
Symmetric Group ◽  
Hopf Algebras ◽  
Symmetric Functions ◽  
Tensor Products ◽  
Ring Structure ◽  
Algebra Structure ◽  
Group Representations ◽  
Symmetric Group Representations

The Hopf algebra structure of the ring of symmetric functions is used to prove a new identity for the internal product, i.e., the operation corresponding to the tensor product of symmetric group representations. From this identity, or by similar techniques which can also involve the λ-ring structure, we derive easy proofs of most known results about this operation. Some of these results are generalized.

scholarly journals Search for Young diagrams with large dimensions

2019 ◽  
pp. 33-43
Author(s):  
Vasilii S. Duzhin ◽  
◽  
Anastasia A. Chudnovskaya ◽  
Keyword(s):  
Symmetric Group ◽  
Young Diagram ◽  
Numerical Experiments ◽  
Irreducible Representations ◽  
Young Diagrams ◽  
Maximum Dimension ◽  
Asymptotic Combinatorics

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.

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