A Study of the Growth of the Maximum and Typical Normalized Dimensions of Strict Young Diagrams

Vasiliev, N. N.; Duzhin, Vasilii

doi:10.1007/s10958-016-2887-x

Cited by 5 publications

(12 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first diagrams of this sequence match all known exact maximum diagrams. None of our previous algorithms [4] can improve any diagrams of this sequence. We suppose that most of the diagrams in this sequence are strictly maximum.…”

Section: Maximum Diagrams Searching Algorithmmentioning

confidence: 97%

“…In this paper, we draw the diagrams in the upper right quadrant. Figure 1 illustrates two examples of Young diagrams represented by the partitions (6, 5, 2, 2, 1, 1), (5,4,2,1), respectively. A strict Young diagram is a Young diagram with no columns of the same height.…”

Section: Definitionsmentioning

confidence: 99%

“…Briefly speaking, the bigger sequence improves the smaller one. Earlier in [4] an algorithm which improves any given sequence was introduced. In this paper, we propose a much more efficient technique for constructing sequences of diagrams with large dimensions.…”

Section: Maximum Diagrams Searching Algorithmmentioning

confidence: 99%

“…In contrast with the previous papers [3,4], our study of asymptotic behaviour of normalized dimensions as function of the diagram size is based on the investigation of their finite differences. We study not only the growth but also the oscillations of normalized dimensions in greedy sequences.…”

Section: Study Of Normalized Dimension Asymptotic Behaviour In Greedymentioning

confidence: 99%

“…Let us call the rightmost part of a partition a regular tail if it contains only consecutive odd (..., 7, 5, 3, 1) or consecutive even (..., 8,6,4,2) numbers. We have found out that most of partitions corresponding to Table 2.…”

Section: The Case Of Strict Diagramsmentioning

confidence: 99%

See 4 more Smart Citations

Asymptotic behavior of normalized dimensions of standard and strict Young diagrams — growth and oscillations

Duzhin

Vasilyev

2016

J. Knot Theory Ramifications

Self Cite

View full text Add to dashboard Cite

Asymptotic behaviour of normalized dimensions of standard and strict Young diagrams -growth and oscillations V. Duzhin, N. Vasilyev For citation: V. S. Duzhin, N. N. Vasilyev, Asymptotic behavior of normalized dimensions of standard and strict Young diagrams -growth and oscillations. -J. Knot Theory Ramifications 26 (2016). AbstractIn this paper, we present the results of a computer investigation of asymptotics for maximum dimensions of linear and projective representations of the symmetric group. This problem reduces to the investigation of standard and strict Young diagrams of maximum dimensions. We constructed some sequences for both standard and strict Young diagrams with extremely large dimensions. The conjecture that the limit of normalized dimensions exists was proposed by A. M. Vershik 30 years ago [1] and has not been proved yet.We studied the growth and oscillations of the normalized dimension function in sequences of Young diagrams. Our approach is based on analyzing finite differences of their normalized dimensions. This analysis also allows us to give much more precise estimation of the limit constants.

show abstract

Section: Maximum Diagrams Searching Algorithmmentioning

confidence: 97%