On Blocking Sets in Affine Hjelmslev Planes

ACM Computing Classification System (1998): G.2.1.We prove that the minimum size of an affine blocking set in the affine plane AHG ...This research has been supported by the Scientific Research Fund of Sofia University under Contract No 109/09.05.2012

On arcs in projective Hjelmslev planes

AbstractA (k,n)-arc in the projective Hjelmslev plane PHG(RR3) is defined as a set of k points in the plane such that some n but no n+1 of them are collinear. In this paper, we consider the problem of finding the largest possible size of a (k,n)-arc in PHG(RR3). We present general upper bounds on the size of arcs in the projective Hjelmslev planes over chain rings R with |R|=q2,R/radR≅Fq. We summarize the known values and bounds on the cardinalities of (k,n)-arcs in the chain rings with |R|⩽25(|R|=q2,R/radR≅Fq)

Basic Algorithms for Manipulation of Modules over Finite Chain Rings

In this paper, we present some basic algorithms for manipulation of finitely generated modules over finite chain rings. We start with an algorithm that generates the standard form of a matrix over a finite chain ring, which is an analogue of the row reduced echelon form for a matrix over a field. Furthermore we give an algorithm for the generation of the union of two modules, an algorithm for the generation of the orthogonal module to a given module, as well as an algorithm for the generation of the intersection of two modules. Finally, we demonstrate how to generate all submodules of fixed shape of a given module. ACM Computing Classification System (1998): G.1.3, G.4

Embedding maximal cliques of sets in maximal cliques of bigger sets

AbstractCharacterizations are obtained of the maximal (k + s)-cliques that contain a given maximal k-clique as a substructure: (1) when s = 1; (2) for arbitrary s when no line of the clique contains exactly one point of the subclique. These characterizations are used to obtain maximal cliques which have fewer lines (for given k) than previously known examples