162 research outputs found
On Distance-Regular Graphs with Smallest Eigenvalue at Least
A non-complete geometric distance-regular graph is the point graph of a
partial geometry in which the set of lines is a set of Delsarte cliques. In
this paper, we prove that for fixed integer , there are only finitely
many non-geometric distance-regular graphs with smallest eigenvalue at least
, diameter at least three and intersection number
Partial ovoids and partial spreads in finite classical polar spaces
We survey the main results on ovoids and spreads, large maximal partial ovoids and large maximal partial spreads, and on small maximal partial ovoids and small maximal partial spreads in classical finite polar spaces. We also discuss the main results on the spectrum problem on maximal partial ovoids and maximal partial spreads in classical finite polar spaces
The use of blocking sets in Galois geometries and in related research areas
Blocking sets play a central role in Galois geometries. Besides their intrinsic geometrical importance, the importance of blocking sets also arises from the use of blocking sets for the solution of many other geometrical problems, and problems in related research areas. This article focusses on these applications to motivate researchers to investigate blocking sets, and to motivate researchers to investigate the problems that can be solved by using blocking sets. By showing the many applications on blocking sets, we also wish to prove that researchers who improve results on blocking sets in fact open the door to improvements on the solution of many other problems
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to
distance-regular graphs for the reader who is unfamiliar with the subject, and
then give an overview of some developments in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page
Green's sumset problem at density one half
We investigate the size of subspaces in sumsets and show two main results.
First, if A is a subset of F_2^n with density at least 1/2 - o(n^{-1/2}) then
A+A contains a subspace of co-dimension 1. Secondly, if A is a subset of F_2^n
with density at least 1/2-o(1) then A+A contains a subspace of co-dimension
o(n).Comment: 10 pp. Corrected typo
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