Abstract
A typical problem in extremal combinatorics is the following. Given a large number n and a set L, find the maximum cardinality of a family of subsets of a ground set of n elements such that the intersection of any two subsets has cardinality in L. We investigate the generalization of this problem, where intersections of more than 2 subsets are considered. In particular, we prove that when k−1 is a power of 2, the size of the extremal k-wise oddtown family is (k−1)(n− 2log2(k−1)). Tight bounds are also found in several other basic cases.
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Research supported in part by NSF grant DMS 99-70270 and by the joint Berlin/Zurich graduate program Combinatorics, Geometry, Computation, financed by the German Science Foundation (DFG) and ETH Zürich
Research supported in part by NSF grant DMS-0200357, by an NSF CAREER award and by an Alfred P. Sloan fellowship. webpage: http://www.math.ucsd.edu/vanvu/
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Szabó, T., Vu, V.H. Exact k-Wise Intersection Theorems. Graphs and Combinatorics 21, 247–261 (2005). https://doi.org/10.1007/s00373-005-0609-0
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DOI: https://doi.org/10.1007/s00373-005-0609-0