The fine triangle intersection problem for K4-e-designs

Let F i n ( v ) = { ( s , t ) : ? ?a?pair?of? ( K 4 - e ) -designs?of?order? v ?intersecting?in? s ?blocks?and? 2 s + t ?triangles } . Let A d m ( v ) = { ( s , t ) : s + t ? b v , s ? J ( v ) , 2 s + t ? J T ( v ) } ? { ( b v - 3 , 1 ) } , where J ( v ) (or J T ( v ) ) denotes the set of positive integers s (or t ) such that there exists a pair of ( K 4 - e ) -designs of order v intersecting in s blocks (or t triangles), and b v = v ( v - 1 ) / 10 . It is established that F i n ( v ) = A d m ( v ) for any integer v ? 0 , 1 ( mod 5 ) , v ? 6 and v ? 10 , 11 .

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