Set-systems with prescribed cardinalities for pairwise intersections
Z Füredi - Discrete Mathematics, 1982 - Elsevier
Discrete Mathematics, 1982•Elsevier
Suppose that A is a finite set-system on N points, and for everytwo different A, A′ ϵ A we
have| A∩ A′|= 0 or r. Then we prove that| A≤⌊ N r⌋ 2+⌊ N r⌋+(N− r⌊ N r⌋) whenever N>
N 0 (r). The extremal family is unique and consists of 2r, r and 1-elements sets only. The
assumption N> N 0 (r) can not be omitted. We state some further results and problems.
have| A∩ A′|= 0 or r. Then we prove that| A≤⌊ N r⌋ 2+⌊ N r⌋+(N− r⌊ N r⌋) whenever N>
N 0 (r). The extremal family is unique and consists of 2r, r and 1-elements sets only. The
assumption N> N 0 (r) can not be omitted. We state some further results and problems.
Suppose that A is a finite set-system on N points, and for everytwo different A, A′ ϵ A we have| A∩ A′|= 0 or r. Then we prove that| A≤⌊ N r⌋ 2+⌊ N r⌋+(N− r⌊ N r⌋) whenever N> N 0 (r). The extremal family is unique and consists of 2r, r and 1-elements sets only. The assumption N> N 0 (r) can not be omitted. We state some further results and problems.
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