33 citations · 45 across the 15 of their papers we have counts for
13 papers · 1 filter
Squaring the circle: embedding in
Ian Doust, Anthony Weston
Let be the unit circle endowed with the arc length metric. This paper concerns the question of which subsets of can be embedded isometrically into the sequence…
Polygonal equalities and -negative type
Ian Doust, Anthony Weston
Nontrivial -polygonal equalities impose certain conditions on the geometry of a metric space and so it is of interest to be able to identify the values of $p \in [0,\inf…
Beyond trees: the metric geometry of subsets of weighted Hamming cubes
Ian Doust, Anthony Weston
Associated to any finite metric space are a large number of objects and quantities which provide some degree of structural or geometric information about the space. In this paper w…
Distance matrices of subsets of the Hamming cube
Ian Doust, Gavin Robertson, Alan Stoneham +1
Graham and Winkler derived a formula for the determinant of the distance matrix of a full-dimensional set of points in the Hamming cube…
The geometry of two-valued subsets of -spaces
Anthony Weston
Let denote the algebra of all scalar-valued measurable functions on a measure space . Let be a set of finitely supported m…
A direct proof that has generalized roundness zero
Ian Doust, Stephen Sánchez, Anthony Weston
Metric spaces of generalized roundness zero have interesting non-embedding properties. For instance, we note that no metric space of generalized roundness zero is isometric to any…