6533b86ffe1ef96bd12cdf4e
RESEARCH PRODUCT
On extremal intersection numbers of a block design
Albrecht Beutelspachersubject
CombinatoricsDiscrete mathematicsIntersectionHyperplaneDiscrete Mathematics and CombinatoricsProjective spaceIntersection numberFinite intersection propertyMajumdarTheoretical Computer ScienceMathematicsBlock designdescription
K.N. Majumdar has shown that for a 2-(v, k, @l) design D there are three numbers @a, @t, and @S such that each intersection number of D is not greater than @S and not less than max{@a, @t}. In this paper we investigate designs having one of these 'extremal' intersection numbers. Quasisymmetric designs with at least one extremal intersection number are characterized. Furthermore, we show that a smooth design D having the intersection number @S or @a>0 is isomorphic to the system of points and hyperplanes of a finite projective space. Using this theorem, we can characterize all smooth strongly resolvable designs.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1982-01-01 | Discrete Mathematics |