We apply the new orbifold duality transformations to discuss the special case of cyclic coset orbifolds in further detail. We focus in particular on the case of the interacting cyclic coset orbifolds, whose untwisted sectors are Zλ(permutation)-invariant g/h coset constructions which are not λ copies of coset constructions. Because λ copies are not involved, the action of Zλ(permutation) in the...

This project is appropriate for someone with an interest in both group theory and algorithms. Familiarity with basic group theory is essential. A group may be described very compactly via a presentation by generators and relations. For example, the alternating group A5 of order 60 is isomorphic to 〈x, y | x = y = (xy) = 1〉. However, it is not usually easy to study a group given by a presentatio...

A new method for coset enumeration in symmetrically generated groups is presented. This method is based on a Gröbner bases algorithm applied to polynomials in non-commuting variables with integer coefficients. Mathematics Subject Classification: 05A05; 20B05; 20B40

In order to calculate the error probability of a code it is necessary to know the distribution of the coset leaders. The enumeration of cosets of the first order Reed Muller code has been studied (i) by Berlekamp and Welch (1972) by associating with each coset a class of Boolean functions, and (ii) by Sloane and Dick (1971) by associating with each coset a class of single-error-correcting codes...

Jacobi polynomials were introduced by Ozeki in analogy with Jacobi forms of lattices They are useful for coset weight enumeration and weight enumeration of children We determine them in most interesting cases in length at most and in some cases in length We use them to construct group divisible designs packing designs covering designs and t r designs in the sense of Calderbank Delsarte A major ...

The well-known Todd-Coxeter algorithm [14], which may be viewed as a means of constructing permutation representations of finitely presented groups, remains a primary reference for coset enumeration programs. All the strategies and variants of this algorithm perform essentially the same calculations as the original algorithm, merely choosing different orders in which to process the available in...