We refine previous results to provide examples, and in some cases precise classifications, of extremal subsets of {1, ..., n} containing no solutions to a wide class of non-inva...
Suppose we toss an independent coin with probability of success p for each subset of [n] = {1, . . . , n}, and form the random hypergraph P(n, p) by taking as hyperedges the subse...
Consider a k-element subset P of the plane. It is known that the maximum number of sets similar to P that can be found among n points in the plane is (n2 ) if and only if the cros...
Background: Molecular profiling generates abundance measurements for thousands of gene transcripts in biological samples such as normal and tumor tissues (data points). Given such...