Distance matrices of subsets of the Hamming cube

@article{Doust2020DistanceMO,
title={Distance matrices of subsets of the Hamming cube},
author={Ian Doust and G. Neil Robertson and Alan Stoneham and Anthony Weston},
journal={arXiv: Functional Analysis},
year={2020}
}
• I. Doust, +1 author A. Weston
• Published 19 May 2020
• Mathematics
• arXiv: Functional Analysis
Graham and Winkler derived a formula for the determinant of the distance matrix of a full-dimensional set of $n + 1$ points $\{ x_{0}, x_{1}, \ldots , x_{n} \}$ in the Hamming cube $H_{n} = ( \{ 0,1 \}^{n}, \ell_{1} )$. In this article we derive a formula for the determinant of the distance matrix $D$ of an arbitrary set of $m + 1$ points $\{ x_{0}, x_{1}, \ldots , x_{m} \}$ in $H_{n}$. It follows from this more general formula that $\det (D) \not= 0$ if and only if the vectors $x_{0}, x_{1… Expand 2 Citations Roundness Properties of Banach spaces • Mathematics • 2021 The maximal roundness of a metric space is a quantity that arose in the study of embeddings and renormings. In the setting of Banach spaces, it was shown by Enflo that roundness takes on a muchExpand The maximal generalised roundness of finite metric spaces We provide two simplifications of Sanchez's formula for the maximum generalised roundness of a finite metric space. References SHOWING 1-10 OF 31 REFERENCES Distance matrices of subsets of the Hamming cube • Indag. Math. 32 • 2021 On the gap of finite metric spaces of p-negative type Let (X,d) be a metric space of p-negative type. Recently I. Doust and A. Weston introduced a quantification of the p-negative type property, the so called gap {\Gamma} of X. This talk introduces someExpand Finite quasihypermetric spaces • Mathematics • 2009 AbstractLet (X, d) be a compact metric space and let $$\mathcal{M}$$(X) denote the space of all finite signed Borel measures on X. Define I: $$\mathcal{M}$$(X) → ℝ by I(μ) = ∫X∫Xd(x,Expand The maximal generalised roundness of finite metric spaces We provide two simplifications of Sanchez's formula for the maximum generalised roundness of a finite metric space. Estimating the gap of finite metric spaces of strict p-negative type • R. Wolf • Mathematics • Linear Algebra and its Applications • 2018 Let (X,d) be a finite metric space. This paper first discusses the spectrum of the p-distance matrix of a finite metric space of p-negative type and then gives upper and lower bounds for the soExpand Euclidean Distance Matrices: Essential theory, algorithms, and applications • Computer Science, Mathematics • IEEE Signal Processing Magazine • 2015 The fundamental properties of EDMs, such as rank or (non)definiteness, are reviewed, and it is shown how the various EDM properties can be used to design algorithms for completing and denoising distance data. Expand Euclidean Distance Geometry and Applications • Mathematics, Biology • SIAM Rev. • 2014 The theory of Euclidean distance geometry and its most important applications are surveyed, with special emphasis on molecular conformation problems. Expand Supremal p-negative type of vertex transitive graphs Abstract We study the supremal p-negative type of connected vertex transitive graphs. The analysis provides a way to characterize subsets of the Hamming cube { 0 , 1 } n ⊂ l 1 ( n ) ( n ⩾ 1 ) thatExpand On the supremal$p$-negative type of a finite metric space We study the supremal$p$-negative type of finite metric spaces. An explicit expression for the supremal$p$-negative type$\wp (X,d)$of a finite metric space$(X,d)\$ is given in terms itsExpand
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Let ( X , d ) be a compact metric space and let ℳ( X ) denote the space of all finite signed Borel measures on  X . Define I :ℳ( X )→ℝ by and set M ( X )=sup I ( μ ), where μ ranges over theExpand