Year: 2006
Type: article
Abstract: We study two combinatorial design problems: finding small $t$-fold blocking sets in $PG(2,q)$ for $q$ prime, and finding large caps in $PG(n,q)$. These problems are combinatorially difficult, but their problem sizes can be reduced by prescribing a group of automorphisms in order to take advantage of the anticipated symmetry of the solution sets. Using this method, a new family of 2-fold blocking sets of size $3q+1$ was discovered. These new sets have the additional property that their complement is also a 2-fold blocking set. For caps, a backtracking algorithm with pruning was developed to solve the resulting 0-1 int eger linear programming problem, and was implemented using C. This algorithm takes advantage of the small size of the right-hand side of the constraints in the LP problem. Also presented is an introduction to finite projective geometries and group actions and the application of group actions to projective geometries.
Source: Summit (Simon Fraser University)
Author: Joanna Lynn Wallis
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2228816501