Intersection families and Snevily's conjecture

Authors:
Kyung-Won Hwang;Naeem N. Sheikh
Affiliations:
Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, IL 61801, USA;Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, IL 61801, USA
Venue:
European Journal of Combinatorics
Year:
2007

Citing 3
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Abstract

Let K={k"1,k"2,...,k"r} and L={l"1,l"2,...,l"s} be sets of nonnegative integers with k"is-r. Let F={F"1,F"2,...,F"m} be a family of subsets of [n] with |F"i|@?K for each i and |F"i@?F"j|@?L for any ij. We prove that |F|@?@?"i"="s"-"r^sn-1i when we have the conditions that |F"i|@?L and k"i's are consecutive. We also prove the same bound under the condition @?"i"="1^mF"i0@? instead of the above conditions. Finally, an observation gives us a bound of n@?n2@? on |F| when K@?L=0@?.