An extended triple system with no idempotent element (ETS) is a collection of non ordered triples of type {x,y,z} or {x,x,y} chosen from a v - set in such a way that each pair (whether di stinct or not ) is contained in exactly one triple . (For example ,in the block {x,x,y}, the pair {x,y} is said to occur one time . ) Such a design has s_v = v(v + 3) /6 blocks and a necessary and sufficient condition for existence is that v = 0 (mod 3). Let J( v) denote the set of non - negative integers k such that there exist two ETS(v) wi th precisely k blocks in common. In this paper we determine J(v) for all admissibl e v, in particular we show that J(9)=I(9)-{13} and J(v) =I(v), where l{v) ={0,1 ... , s _v -3, s_v} .

### A class of extended triple systems and numbers of common triples

#### Abstract

An extended triple system with no idempotent element (ETS) is a collection of non ordered triples of type {x,y,z} or {x,x,y} chosen from a v - set in such a way that each pair (whether di stinct or not ) is contained in exactly one triple . (For example ,in the block {x,x,y}, the pair {x,y} is said to occur one time . ) Such a design has s_v = v(v + 3) /6 blocks and a necessary and sufficient condition for existence is that v = 0 (mod 3). Let J( v) denote the set of non - negative integers k such that there exist two ETS(v) wi th precisely k blocks in common. In this paper we determine J(v) for all admissibl e v, in particular we show that J(9)=I(9)-{13} and J(v) =I(v), where l{v) ={0,1 ... , s _v -3, s_v} .
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1995
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11570/2036505`
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