Mathematical Research Seminar - Archive

We show that many infinite classes of permutations over finite fields can be constructed via translators with a large choice of parameters. We characterize some functions having linear translators, based on which several families of permutations are then derived. We give in several cases the compositional inverse of these permutations. The connection with complete permutations is also utilized to provide further infinite classes of permutations.

In this talk we'll describe some properties of certain discrete subgroups of quaternionic matrices acting in the hyperbolic quaternionic space which are similar to the modular group in the complex case: we highlight similarities and differences. This work is in collaboration with J.P Diaz Gonzalez and A. Verjovsky (UNAM Cuernavaca, Mexico)

We study codes spanned by the rows of an orbit matrix of a symmetric design with respect to an automorphism group that acts with all orbits of the same length. The dimension of such codes is discussed. We define an extended orbit matrix and show that under some condition the rows of the extended orbit matrix span a code that is self-dual with respect to a certain scalar product.

Based on joint work with Dean Crnković.

A graph G is said to be 1-perfectly orientable (1-p.o. for short) if it admits an orientation such that the out-neighborhood of every vertex is a clique in G. The class of 1-p.o. graphs forms a common generalization of the classes of chordal and circular arc graphs. Even though 1-p.o. graphs can be recognized in polynomial time, no structural characterization of 1-p.o. graphs is known. In this paper we consider the four standard graph products: the Cartesian product, the strong product, the direct product, and the lexicographic product. For each of them, we characterize when a nontrivial product of two graphs is 1-p.o.

Based on joint work with Martin Milanič.