In the last couple of years many research papers have been devoted to Abelian complexity of words. Recently, Constantinescu and Ilie (Bulletin EATCS 89, 167–170, 2006) introduced the notion of Abelian period. In this article we present two quadratic brute force algorithms for computing Abelian periods for special cases and a quasi-linear algorithm for computing all the Abelian periods of a word.

We show that every semi-abelian category, as defined by Palamodov, possesses a maximal exact structure in the sense of Quillen and that the exact structure of a quasi-abelian category is a special case thereof.

We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read–Rezayi state whose effective theory is the SU(2)K Chern–Simons theory. As a generalization of the Pfaffian (K = 2) and the Fibonacci (K = 3) anyon states, we compute the braiding matrices of quasi-particle states with arbitrary spins. Furthermore we prop...

We study the question of the validity of the Snake Lemma in a P-semi-abelian category. We also obtain a generalization of the Snake Lemma in a quasi-abelian category. Mathematics Subject Classification: 18A20, 18E05.

To characterize categorical constraints associativity, commutativity and monoidality in the context of quasimonoidal categories, from a cohomological point of view, we define the notion of a parity (quasi)complex. Applied to groups gives non-abelian cohomology. The categorification functor from groups to monoidal categories provides the correspondence between the respective parity (quasi)comple...

A class of self-dual quasi-abelian codes index 2 over any finite field $F$ is introduced. By counting the number such and in this whose relative minimum weights are small, proved to be asymptotically good provided ?1 a square . Moreov...