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Paper   IPM / M / 11164
School of Mathematics
  Title:   Trades and t-designs
  Author(s): 
1.  G. B.. Khosrovshahi
2.  B. Tayfeh-Rezaie
  Status:   In Proceedings
  Proceeding: Surveys in combinatorics 2009
  Vol.:  365
  Year:  2009
  Pages:   91-112
  Editor:  S. Huczynska, C. M. Roney-Dougal, J. D. Mitchell
  Publisher(s):   Cambridge University Press, Cambridge
  Supported by:  IPM
  Abstract:
Trades, as combinatorial objects, possess interesting combinatorial and algebraic properties and play a considerable role in various areas of combinatorial designs. In this paper we focus on trades within the context of t-designs. A pedagogical review of the applications of trades in constructing halving t-designs is presented. We also consider (N,t)-partitionable sets as a generalization of trades. This generalized notion provides a powerful approach to the construction of large sets of t-designs. We review the main recursive constructions and theorems obtained by this approach. Finally, we discuss the linear algebraic representation of trades and present two applications.

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