Union of shadows
A discussion on the union of shadows is presented. It was shown that if A is a family of (3k) 3-sets then there are at least ( 4k) 4-sets that may be written as unions of two 2-sets in the shadow of A. This is the first non-trivial case of a more general conjecture about unions of shadows.
Theoretical Computer Science
Bollobás, B., & Leader, I. (2003). Union of shadows. Theoretical Computer Science, 307 (3), 493-502. https://doi.org/10.1016/S0304-3975(03)00233-0