836 citations
- Macquarie UniversityAU13 papers
- Centre for Quantum Computation and Communication TechnologyAU9 papers
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- Institute of Astronomy and Astrophysics, Academia SinicaTW4 papers
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- Australia Telescope National FacilityAU3 papers
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4 papers · 1 filter
Minimal Euclidean representations of graphs
Aidan Roy
A simple graph G is said to be representable in a real vector space of dimension m if there is an embedding of the vertex set in the vector space such that the Euclidean distance b…
Unitary designs and codes
Aidan Roy, A. J. Scott
A unitary design is a collection of unitary matrices that approximate the entire unitary group, much like a spherical design approximates the entire unit sphere. In this paper, we…
Bounds for codes and designs in complex subspaces
Aidan Roy
We introduce the concepts of complex Grassmannian codes and designs. Let G(m,n) denote the set of m-dimensional subspaces of C^n: then a code is a finite subset of G(m,n) in which…
On Gale and braxial polytopes
Margaret M. Bayer, Tibor Bisztriczky
Cyclic polytopes are characterized as simplicial polytopes satisfying Gale's evenness condition (a combinatorial condition on facets relative to a fixed ordering of the vertices).…