This paper surveys some recent results on the generation of implicitly given hypergraphs and their applications in Boolean and integer programming, data mining, reliability theory, and combinatorics. Given a monotone property π over the subsets of a finite set V , we consider the problem of incrementally generating the family Fπ of all minimal subsets satisfying property π, when π is given by a...

We continue the study of k-monotone Boolean functions in the property testing model, initiated by Canonne et al. (ITCS 2017). A function f : {0, 1} → {0, 1} is said to be kmonotone if it alternates between 0 and 1 at most k times on every ascending chain. Such functions represent a natural generalization of (1-)monotone functions, and have been recently studied in circuit complexity, PAC learni...

We prove a lower bound of (n4/3 log1/3 n) on the randomized decision tree complexity of any nontrivial monotone n-vertex graph property, and of any nontrivial monotone bipartite graph property with bipartitions of size n. This improves the previous best bound of(n4/3) due to Hajnal [Haj91]. Our proof works by improving a graph packing lemma used in earlier work, and this improvement in turn s...

We study tent spaces on general measure spaces (Ω, μ). We assume that there exists a semigroup of positive operators on Lp(Ω, μ) satisfying a monotone property but do not assume any geometric/metric structure on Ω. The semigroup plays the same role as integrals on cones and cubes in Euclidean spaces. We then study BMO spaces on general measure spaces and get an analogue of Fefferman’s H1-BMO du...

This paper studies monotonicity and convexity properties of option prices in jump-diffusion models. In such models it is possible for a monotone contract function to give rise to an option price which is non-monotone in the underlying asset. This is connected to the fact that the no-crossing property, which holds for one-dimensional diffusions, may fail in the presence of jumps. We present a si...