I. Doust

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math.FA2026

Squaring the circle: embedding $S^{1}$ in $ℓ_{1}$

Ian Doust, Anthony Weston

Let $(S^{1}, δ)$ be the unit circle endowed with the arc length metric. This paper concerns the question of which subsets of $(S^{1}, δ)$ can be embedded isometrically into the sequence…

math.FA2024

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…

math.FA2024

Polygonal equalities and $p$ -negative type

Ian Doust, Anthony Weston

Nontrivial $p$ -polygonal equalities impose certain conditions on the geometry of a metric space $(X, d)$ and so it is of interest to be able to identify the values of $p \in [0,\inf…

Squaring the circle: embedding S1 in ℓ1​

Beyond trees: the metric geometry of subsets of weighted Hamming cubes

Polygonal equalities and p-negative type

Squaring the circle: embedding $S^{1}$ in $ℓ_{1}$

Polygonal equalities and $p$ -negative type