Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A flor in a Steiner system is the set of all blocks containing a given point. The flor intersection problem for Steiner systems is the determination of all pairs (v,s) such that there exists a pair of Steiner systems (X,B"1) and (X,B"2) of order v having a common flor F satisfying |(B"1@?F)@?(B"2@?F)|=s.  the flor intersection problem for a pair of S(2,4,v)'s is investigated. Let J(u)={s:@? a pair of S(2,4,3u+1)'s intersecting in s+u blocks, u of them being the blocks of a common flor}. Let I(u)={0,1,...,f"u-8,f"u-6,f"u}, where f"u=3u(u-1)/4 and f"u+u is the number of blocks of an S(2,4,3u+1). It is established that J(u)=I(u) for any positive integer u=0,1(mod4) and u 5,8,9,12.
['Guizhi Zhang', 'Yanxun Chang', 'Tao Feng']
I am writing a research paper on a idea The flower intersection problem for S(2,4,v)'s
[{"from": "human", "value": "I am writing a research paper on a idea The flower intersection problem for S(2,4,v)'s"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A flor in a Steiner system is the set of all blocks containing a given point. The flor intersection problem for Steiner systems is the determination of all pairs (v,s) such that there exists a pair of Steiner systems (X,B\"1) and (X,B\"2) of order v having a common flor F satisfying |(B\"1@?F)@?(B\"2@?F)|=s.  the flor intersection problem for a pair of S(2,4,v)'s is investigated. Let J(u)={s:@? a pair of S(2,4,3u+1)'s intersecting in s+u blocks, u of them being the blocks of a common flor}. Let I(u)={0,1,...,f\"u-8,f\"u-6,f\"u}, where f\"u=3u(u-1)/4 and f\"u+u is the number of blocks of an S(2,4,3u+1). It is established that J(u)=I(u) for any positive integer u=0,1(mod4) and u 5,8,9,12."}]