The standard genetic code multiplet structure as well as the correct degeneracies, class by class, are all extracted from the (unique) number 23!, the order of the permutation group of 23 objects.

We study a family of permutations of the finite field Fqn given by x + γ f(x), where γ ∈ Fqn and f : Fqn → Fq. In particular, we determine the cycle structure and the inverse of such a permutation.

Index 74 Preface The three subjects of the title (codes, matroids, and permutation groups) have many interconnections. In particular, in each case, there is a polynomial which captures a lot of information about the structure: we have the weight enumerator of a code, the Tutte polynomial (or rank polynomial) of a matroid, and the cycle index of a permutation group. With any code is associated a...

Xiaomin Zhang Department of Mathematics, Linyi Normal University, Shandong 276005, China E-mail: [email protected] Abatract The aim of this paper is to study eventually strong wrpp semigroups whose idempotents satisfy permutation identities, that is, so-called PI-strong wrpp semigroups. After some properties are obtained, the structure of such semigroups are investigated. In particular, the struct...

By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d. sequences. This observation not only explains the remarkable properties of lacunary trigonometric series, but also provides a powerful tool in many areas of analysis, such the theory of orthogonal series and Banach space theory. In contrast to i.i.d. sequenc...

Many combinatorial optimization problems can be formulated as the search for the best possible permutation of a given set of objects, according to a given objective function. The corresponding MIP formulation is thus typically made of an assignment substructure, plus additional constraints and variables (as needed) to express the objective function. Unfortunately, the permutation structure is g...

Sorting by Transpositions is an NP-hard problem for which several polynomial-time approximation algorithms have been developed. Hartman and Shamir (2006) developed a 1.5-approximation [Formula: see text] algorithm, whose running time was improved to O(nlogn) by Feng and Zhu (2007) with a data structure they defined, the permutation tree. Elias and Hartman (2006) developed a 1.375-approximation ...