37 citations · 40 across the 9 of their papers we have counts for
12 papers
Submodular and strongly submodular functions and diversities
David Bryant, Paul F. Tupper
Submodular functions and their close relatives play a key role in combinatorial optimization, decision theory and potential theory. Part of their importance and usefulness stems fr…
Linear and Sublinear Diversities
David Bryant, Paul Tupper
Diversities are an extension of the concept of a metric space which assign a non-negative value to every finite set of points, rather than just pairs. A general theory of diversiti…
Diversities and the Generalized Circumradius
David Bryant, Katharina T. Huber, Vincent Moulton +1
The generalized circumradius of a set of points with respect to a convex body equals the minimum value of such that is contained in a t…
Lattice Diversities
David Bryant, Raúl Felipe, Mauricio Toledo-Acosta +1
Diversities are a generalization of metric spaces, where instead of the non-negative function being defined on pairs of points, it is defined on arbitrary finite sets of points. Di…
Fraïssé Limits for Relational Metric Structures
David Bryant, André Nies, Paul Tupper
The general theory developed by Ben Yaacov for metric structures provides Fraïssé limits which are approximately ultrahomogeneous. We show here that this result can be strengthened…
Inner products for Convex Bodies
David Bryant, Petru Cioica-Licht, Lisa Orloff Clark +1
We define a set inner product to be a function on pairs of convex bodies which is symmetric, Minkowski linear in each dimension, positive definite, and satisfies the natural analog…