In 1997 Clarke, Han, and Zeng introduced a q-analogue of Euler’s difference table for n! using a key bijection Ψ on symmetric groups. In this paper we extend their results to the wreath product of a cyclic group with the symmetric group. By generalizing their bijection Ψ we prove the equidistribution of the triple statistics (fix, exc, fmaj) and (fix, exc, fmaf) on wreath products, where “fix”,...

We associate a modal operator with each language belonging to a given class of regular languages and use the (reverse) wreath product of monoids with distinguished generators to characterize the expressive power of the resulting logic.

This paper is concerned with finite primitive permutation groups G which are subgroups of wreath products W in product action and are such that the socles of G and W are the same. The aim is to explore how the study of such groups may be reduced to the study of smaller groups. The O'Nan-Scott Theorem (see Liebeck, Praeger, Saxl [12] for the most recent and detailed treatment) sorts finite primi...

In this paper, we present a new extension of the butterfly digraph, which is known as one of the topologies used for interconnection networks. The butterfly digraph was previously generalized from binary to d-ary. We define a new digraph by adding a signed label to each vertex of the d-ary butterfly digraph. We call this digraph the dihedral butterfly digraph and study its properties. Furthermo...

Symmetry (similarity under transformation) in sensorimotor data streams can be used to derive and represent concepts from percepts, and exploit them in a cognitive framework. This entails finding mechanisms to extract symmetries out of sensorimotor data and convert them into intuitive representations; ”intuitive” implying that the representations created should have a semantic meaning to them. ...

We consider the distance enumerator ∆G(x) of a finite permutation group G, which is the polynomial ∑ g∈G xn−π(g), where n is the degree of G and π(g) the number of fixed points of g ∈ G. In particular, we introduce a bivariate polynomial which is a special case of the cycle index of G, and from which ∆G(x) can be obtained, and then use this new polynomial to prove some identities relating the d...