Intersection theorems and mod p rank of inclusion matrices
Journal of Combinatorial Theory Series A
Multilinear polynomials and Frankl-Ray-Chaudhuri-Wilson type intersection theorems
Journal of Combinatorial Theory Series A - Series A
On generalizations of the deBruijn-Erdo¨s theorem
Journal of Combinatorial Theory Series A
Proof of a conjecture of Frankl and Füredi
Journal of Combinatorial Theory Series A
Intersection families and Snevily's conjecture
European Journal of Combinatorics
Algebraic properties of modulo q complete ℓ-wide families
Combinatorics, Probability and Computing
Set systems with restricted k-wise L -intersections modulo a prime number
European Journal of Combinatorics
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Alon, Babai and Suzuki proved the following theorem:iLet p be a prime and let K, iL be two disjoint subsets of {0, 1, … , ip − 1}. iLet |iK| = ir, |iL| = is, iand assume r(is − r + 1) ≤ ip − 1 iand n ≥ is + kr where kr is the maximal element of K. Let {\cal F} ibe a family of subsets of an n-element set. Suppose that(i) |iF| ∈ iK (mod ip) ifor each F ∈ {\cal F};(ii) |iE {\cap} iF| ∈ iL (mod ip) ifor each pair of distinct sets E, iF ∈ {\cal F}.iThen |{\cal F}| \leq ({n\atop s}) + ({n\atop s-1}) + \cdots + ({n\atop s-r+1}).They conjectured that the condition that ir(is − r + 1) ≤ ip − 1 in the theorem can be dropped and the same conclusion should hold. In this paper we prove that the same conclusion holds if the two conditions in the theorem, i.e. ir(is − r + 1) ≤ ip − 1 and in ≥ is + ikr are replaced by a single more relaxed condition 2is − ir ≤ in.