Combinatorial Topology and Trade Off Method in BIB Designs.
ILLINOIS UNIV AT CHICAGO CIRCLE DEPT OF MATHEMATICS
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When two BIB designs based on the same set of varieties have identical parameters, one can obtain either of them from the other by trading off some blocks for an equal number of blocks. Define a trade to be two collections of blocks such that each of the v2 pairs of varieties is contained in the same number of blocks from both collections. A method, based on combinatorial topology, for studying the trades with block size 3 is introduced. Using this method it is proven that the volume of a trade can never be 5. Also we present a simple topological proof of the existence of a unique type of minimal trades, into which every trade can be decomposed.
- Statistics and Probability