A simple replacement approach is used to construct new symmetric and affine designs from projective or affine spaces. This is used to construct symmetric designs with a given autom...
A striking result of Bouc gives the decomposition of the representation of the symmetric group on the homology of the matching complex into irreducibles that are self-conjugate. We...
A design is a finite set of points in a space on which every "simple" functions averages to its global mean. Illustrative examples of simple functions are low-degree pol...
We present various techniques to count proportions of permutations with restricted cycle structure in finite permutation groups. For example, we show how a generalized block theo...
In this survey a novel system, called the oscillator system, consisting of order of p3 functions (signals) on the finite field Fp, is described and studied. The new functions are p...