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let A={1,2,3...,N} $A=\{1,2,3...,N\}$ and B1,B2,B3..,Bn $B_1,B_2,B_3\dots,B_n$ be a series of subsets of A $A$ which satisfied that |Bi|=m |Bi∩Bj|<=k. $|B_i|=m$, $|B_i\cap B_j|\le k$. what is the maximum of n? $n$? (k$k< m< NN$)

it can be easily showed that n⩽ $n\le [C(N−1,k)/C(m−1,k)]/[N/m] C(N−1,k)/C(m−1,k)]/[N/m]$ (by counting twice,[X] twice, $[X]$ is integer part of x)$x$)

I wonder is there any reserch that tackle this problem? Do we have some profound result?

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let A={1,2,3...,N} and B1,B2,B3..,Bn be a series of subsets of A which satisfied that |Bi|=m |Bi∩Bj|<=k. what is the maximum of n? (k< m< N)

it can be easily showed that n⩽ [C(N−1,k)/C(m−1,k)]/[N/m] (by counting twice,[X] is integer part of x)

I wonder is there any reserch that tackle this problem? Do we have some profound result?

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# set and subset series combinatorics

let A={1,2,3...,N} and B1,B2,B3..,Bn be a series of subsets of A which satisfied that |Bi|=m |Bi∩Bj|<=k. what is the maximum of n? (k

it can be easily showed that n⩽ [C(N−1,k)/C(m−1,k)]/[N/m] (by counting twice,[X] is integer part of x)

I wonder is there any reserch that tackle this problem? Do we have some profound result?