Combinatorial Topology and Trade Off Method in BIB Designs.

Abstract

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 (v/2) 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.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1978
Accession Number
ADA061926

Entities

People

  • A. S. Hedayat
  • Shuo-yen Robert Li

Organizations

  • University of Illinois at Chicago

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Communities of Interest

  • Air Platforms

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  • Air Force
  • Algebraic Topology
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  • Illinois
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Fields of Study

  • Mathematics

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