On maximum intersecting sets in direct and wreath product of groups

Automorphism Groups of Wreath Product Digraphs

We strengthen a classical result of Sabidussi giving a necessary and sufficient condition on two graphs, X and Y , for the automorphsim group of the wreath product of the graphs, Aut(X o Y ) to be the wreath product of the automorphism groups Aut(X) o Aut(Y ). We also generalize this to arrive at a similar condition on color digraphs. The main purpose of this paper is to revisit a well-known an...

Automorphisms of Regular Wreath Product p-Groups

We present a useful new characterization of the automorphisms of the regular wreath product group P of a finite cyclic p-group by a finite cyclic p-group, for any prime p, and we discuss an application. We also present a short new proof, based on representation theory, for determining the order of the automorphism group Aut P , where P is the regular wreath product of a finite cyclic p-group by...

Image Processing with Wreath Product Groups

Intersecting Families in the Alternating Group and Direct Product of Symmetric Groups

Let Sn denote the symmetric group on [n] = {1, . . . , n}. A family I ⊆ Sn is intersecting if any two elements of I have at least one common entry. It is known that the only intersecting families of maximal size in Sn are the cosets of point stabilizers. We show that, under mild restrictions, analogous results hold for the alternating group and the direct product of symmetric groups.

The maximum size of intersecting and union families of sets

We consider the maximal size of families of k-element subsets of an n element set [n] = {1, 2, . . . , n} that satisfy the properties that every r subsets of the family have non-empty intersection, and no ` subsets contain [n] in their union. We show that for large enough n, the largest such family is the trivial one of all ( n−2 k−1 ) subsets that contain a given element and do not contain ano...