DOIAbstract
AbstractSuppose m and t are integers such that 0<t⩽m. An (m,t) splitting system is a pair (X,B) where |X|=m,B is a set of ⌊m/2⌋ subsets of X, called blocks such that for every Y⊆X and |Y|=t, there exists a block B∈B such that |B∩Y|=⌊t/2⌋ or |(X⧹B)∩Y|=⌊t/2⌋. We will give some results on splitting systems for t=2 or 4 which often depend on results from uniform separating systems. Suppose that m is an even integer, t1,t2 are integers such that t1+t2⩽m. A uniform (m,t1,t2)-separating system is an ordered pair (X,B) where |X|=m,B is a set of subsets of X of size m/2, called blocks, such that for every P⊆X,Q⊆X where |P|=t1,|Q|=t2 and P∩Q=∅, there exists a block B∈B for which either P⊆B,Q∩B=∅ or Q⊆B,P∩B=∅. We also give new results for separating s...
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