Algebraic combinatorics is the study of combinatorial objects as an extension of the study of
finite permutation groups, or, in other words, group theory without groups. In the spirit of …

A unitary t-design is a powerful tool in quantum information science and fundamental
physics. Despite its usefulness, only approximate implementations were known for general t …

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 use …

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The approximation of probability measures on compact metric spaces and in particular on
Riemannian manifolds by atomic or empirical ones is a classical task in approximation and …

Real spherical designs and real and complex projective designs have been shown by
Delsarte, Goethals, and Seidel to give rise to association schemes when the strength of the …

Maximal antipodal sets of Riemannian manifolds were introduced by the author and T.
Nagano in [Un invariant g\'eom\'etrique riemannien, CR Acad. Sci. Paris S\'er. I Math. 295 …

In this note we apply a spectral method to the graph of alternating bilinear forms. In this way,
we obtain upper bounds on the size of an alternating rank-metric code for given values of …

The construction of optimal line packings in real or complex Euclidean spaces has been
shown to be a tantalizingly difficult task, because it includes the problem of finding maximal …

In this paper, we first provide an inductive construction of designs on compact groups G from
those on subgroups K when (G, K) is a Gelfand pair. We then use the construction to provide …