On Representing Sylvester-Gallai Designs.
On sets of vectors of a finite vector space in which every subset of basis size is a basis
It is shown that the maximum size of a set of vectors of a -dimensional vector space over , with the property that every subset of size is a basis, is at most , if , and at most , if , where and is prime. Moreover, for , the sets of maximum size are classified, generalising Beniamino Segre’s “arc is a conic” theorem. These results have various implications. One such implication is that a matrix, with and entries from , has columns which are linearly dependent. Another is...
On Sidon sequences of even orders
On small distances of small 2-groups
The paper reports the results of a search for pairs of groups of order that can be placed in the distance for the case when . The constructions that are used are of the general character and some of their properties are discussed as well.
On some Generalizations of a Class of Discrete Functions
In this paper we examine discrete functions that depend on their variables in a particular way, namely the H-functions. The results obtained in this work make the “construction” of these functions possible. H-functions are generalized, as well as their matrix representation by Latin hypercubes.
On some hyperbolic planes from finite projective planes.
On some symmetric designs with classical parameters.
On special structure of graphs having the maximal eigenvalue greater than two.
On Spectral Structure Of Graphs Having The Maximal Eigenvalue Not Grater Than Two
On Squashed Designs.
On 's and 's admitting a semiregular automorphism group of order 9.
On strongly sum-free subsets of abelian groups
In his book on unsolved problems in number theory [1] R. K. Guy asks whether for every natural l there exists with the following property: for every and any n elements of a group such that the product of any two of them is different from the unit element of the group, there exist l of the such that for and . In this note we answer this question in the affirmative in the first non-trivial case when l=3 and the group is abelian, proving the following result.
On Subdesigns of Symmetric Designs.
On subdirectly irreducible Steiner loops of cardinality .
On Subdivisions of Simplicial Complexes: Characterizing Local h-Vectors.
On Subgraphs as Matroid Cells.
On sums over partially ordered sets.
On Supplementary Difference Sets.
On swell-colored complete graphs.
On the algebraic form of Keller's conjecture