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|Paper IPM / M / 11164||
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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