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

In 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 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 Vershik 30 years ago [A. M. Vershik and S. V. Kerov, Funktsional Anal. i Prilozhen 19(1) (1985) 25–36] 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.

Computer Investigation of Tensioned Fabric Structure in the Form of Enneper Minimal Surface

Form-finding of tensioned fabric structure in the form of Enneper minimal surface has been investigated. Computational form-finding is frequently used to investigate the possible forms of uniformly stressed surfaces. In this study, two parameter of Enneper minimal surface was used in this study are u and v = 0.4 and 1.2. This study provides an alternative choice for engineer to consider the Enneper minimal surface, u = v = 0.4 and 1.2 to be applied in tensioned fabric structure.

Studying the Polypeptide Sequence (α-Code) of Escherichia coli

This paper is devoted to algebraically simulating the α-code of bacterium Escherichia coli and studying contrast factors (words) in its polypeptide sequence. We utilize the methods of spectral theory of graphs which were previously employed by us for enumerating De Bruijn and Kautz sequences. The empirical material is borrowed from the computer investigation of contrast factors in the polypeptide sequences of prokaryotes.