Let ). < i, be infinite cardinals and let Q be a set of cardinality 'c. The bounded permutation group B. (Q), or simply B2, is the group consisting of all permutations of Q which move fewer than A points in Q. We say that a permutation group G acting on Q is a supplement of B2 if BA G is the full symmetric group on Q. In [7], Macpherson and Neumann claimed to have classified all supplements of ...

This paper introduces the concept of orbit-homogeneity of permutation groups: a group G is orbitt-homogeneous if two sets of cardinality t lie in the same orbit of G whenever their intersections with each G-orbit have the same cardinality. For transitive groups, this coincides with the usual notion of t-homogeneity. This concept is also compatible with the idea of partition transitivity introdu...

using elementary permutations also called modules These modules have a simple structure and are based on internal smaller permutations Two cases are considered In the rst the modules apply internal permutations only It has been proved that the composition of modules generates the alternating group for the number of binary inputs bigger than In the second DES like modules are considered and it i...

Let G(q) be the group of permutations of Fq generated by those permutations which can be represented as c 7→ ac + bc with a, b ∈ Fq and 0 < m < n < q. We show that there are infinitely many q for which G(q) is the group of all permutations of Fq . This resolves a conjecture of Vasilyev and Rybalkin.

Every permutation group which is not 2-transitive acts on a nontrivial coherent configuration, but the question of which permutation groups G act on nontrivial association schemes (symmetric coherent configurations) is considerably more subtle. A closely related question is: when is there a unique minimal G-invariant association scheme? We examine these questions, and relate them to more famili...

shuffle product of the permutations u E E k and v' E E k, we mean the following element from ~+~, /,, (i), i < k , vmv'=: Z o'o(~,| where (v~v') ( i ) = ~ . v , ( i _ k ) + l e ' i ' > k . a(~sk+n'cn} Since the permutations form an additive basis of the space ~ , the shuffle multiplication is uniquely extended "by linearity" to any pair of elements from ~ and defines in $ = ~0$n a structure of ...

Analytical approaches to musical analysis have generally attempted to provide some kind of justification, and, in the last decades, to develop analytical elements based on tesselations of pitch class sets. When applied to atonal music, analytical approaches frequently fail to find internal coherence. Most of the time, tilings of chords are based on a torus representation, which follows the trad...

Proof. (5.2) implies that the set of permutations is closed under com­ position of functions. We check the three axioms for a group. We already proved that composition of functions is associative. Let i : S −→ S be the identity function from S to S. Let f be a permutation of S. Clearly f ◦ i = i ◦ f = f . Thus i acts as an identity. Let f be a permutation of S. Then the inverse g of f is a perm...