OFFSET
4,1
COMMENTS
Maximum number of K_4^3's that can be packed in a doubled K_n^3, where K_n^m is the complete m-uniform hypergraph on n vertices.
LINKS
Richard K. Guy, A problem of Zarankiewicz, Research Paper No. 12, Department of Mathematics, University of Calgary, January 1967. [Annotated and scanned copy, with permission]
Haim Hanani, On quadruple systems, Canadian Journal of Mathematics, 12 (1960), 145-157.
Jeremy Tan, An attack on Zarankiewicz's problem through SAT solving, arXiv:2203.02283 [math.CO], 2022.
FORMULA
a(n) >= 2*A001843(n). Equality holds if n = 6k+2 or 6k+4 (Hanani).
EXAMPLE
a(6) = 9 because of the following optimal collection of 4-subsets:
1 2 3 4
2 3 4 5
3 4 5 6
4 5 6 1
5 6 1 2
6 1 2 3
1 2 4 5
2 3 5 6
3 4 6 1
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Jeremy Tan, Jan 31 2022
STATUS
approved