On a conjecture of Frankl and Füredi.
On a two-sided Turán problem.
On cross-intersecting uniform sub-families of hereditary families.
On hypergraphs of girth five.
On hypergraphs with every four points spanning at most two triples.
On non-intersecting arithmetic progressions
We improve known bounds for the maximum number of pairwise disjoint arithmetic progressions using distinct moduli less than x. We close the gap between upper and lower bounds even further under the assumption of a conjecture from combinatorics about Δ-systems (also known as sunflowers).
On randomly generated intersecting hypergraphs.
On randomly generated non-trivially intersecting hypergraphs.
On sets of integers containing k elements in arithmetic progression
On the most weight vectors in a dimension binary code.