We present non-extreme generalisations of intersecting p-brane solutions of eleven-dimensional supergravity which upon toroidal compactification reduce to non-extreme static black holes in dimensions D = 4, D = 5 and 6 ≤ D ≤ 9, parameterized by four, three and two charges, respectively. The D = 4 black holes are obtained either from a non-extreme configuration of three intersecting five-branes ...

A family J of subsets of {1, . . . , n} is called a j-junta if there exists J ⊆ {1, . . . , n}, with |J | = j, such that the membership of a set S in J depends only on S ∩ J . In this paper we provide a simple description of intersecting families of sets. Let n and k be positive integers with k < n/2, and let A be a family of pairwise intersecting subsets of {1, . . . , n}, all of size k. We sh...