We study asymptotics of an irreducible representation of the symmetric group Sn corresponding to a balanced Young diagram λ (a Young diagram with at most O( √ n) rows and columns) in the limit as n tends to infinity. We find an optimal asymptotic bound for characters χ(π). Our main achievement is that—contrary to previous results in this direction—we do not assume that the length |π| of the per...

A basis of symmetric functions, which we denote by q*(X; q, t), was introduced in the work of Ram and King and Wybourne in order to describe the irreducible characters of the Hecke algebras of type A. In this work we give combinatorial descriptions of the expansions of the functions q*(X; q, t) in terms of the classical bases of symmetric functions and apply these results in determining the det...

The permutation entropy concept of Bandt and Pompe (2002 Phys. Rev. Lett. 88 174102) is used to analyze the fluctuations in ion saturation current that spontaneously arise in a basic experimental study (Pace et al 2008 Phys. Plasmas 15 122304) of electron heat transport in a magnetized plasma. From the behavior of the Shannon entropy and the Jensen–Shannon complexity it is found that the underl...

If G is a finite p-solvable group for some prime p, A a solvable subgroup of the automorphism group of G of order prime to |G| such that A stabilises a p-block b of G and acts trivially on a defect group P of b, then there is a Morita equivalence between the block b and its Watanabe correspondent w(b) of CG(A), given by a bimodule M with vertex ∆P and an endo-permutation module as source, which...

this paper presents a new audio encryption algorithm based on permutation and residue number system. in the current approach, signal samples are combined with residue number system through permutation; therefore, a specific noise is generated. then, the audio signal is combined with the noise, generated by the algorithm, to produce a silence signal. for this purpose, the algorithm uses a predef...

A permutation class is splittable if it is contained in the merge of two of its proper subclasses. We characterise the unsplittable subclasses of the class of separable permutations both structurally and in terms of their bases.

Let G be a finite group, p prime, and (K,O,F) p-modular system. We prove that the trivial source ring of OG is isomorphic to coherent G-stable tuples (χP), where χP virtual character K[NG(P)/P], P runs through all p-subgroups G, coherence condition equality certain values. use this result describe group orthogonal units as product unit Burnside fusion system with (φP) homomorphisms NG(P)/P→F×. ...

Archie (1989) and Faith and Cranston (1991) independently developed a parsimony-based randomization test for assessing the quality of a phylogenetic data matrix. Matrix randomization tests have had a mixed reception from phylogeneticists (e.g., Källersjö et al., 1992; Alroy, 1994; Carpenter et al., 1998; Wilkinson, 1998; Siddall, 2001). In general, however, these are well-founded statistical te...