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Complex Hadamard matrices and the spectral set conjecture.

Mihail N. Kolountzakis, Máté Matolcsi (2006)

Collectanea Mathematica

By analyzing the connection between complex Hadamard matrices and spectral sets, we prove the direction "spectral ⇒ tile" of the Spectral Set Conjecture, for all sets A of size |A| ≤ 5, in any finite Abelian group. This result is then extended to the infinite grid Zd for any dimension d, and finally to Rd.

Complexity of hypersubstitutions and lattices of varieties

Thawhat Changphas, Klaus Denecke (2003)

Discussiones Mathematicae - General Algebra and Applications

Hypersubstitutions are mappings which map operation symbols to terms. The set of all hypersubstitutions of a given type forms a monoid with respect to the composition of operations. Together with a second binary operation, to be written as addition, the set of all hypersubstitutions of a given type forms a left-seminearring. Monoids and left-seminearrings of hypersubstitutions can be used to describe complete sublattices of the lattice of all varieties of algebras of a given type. The complexity...

Comportement harmonique des densités conformes et frontière de Martin

Thomas Roblin (2011)

Bulletin de la Société Mathématique de France

Traitant la série de Poincaré d’un groupe discret d’isométries en courbure négative comme un noyau de Green, on établit une théorie du potentiel assez comparable à la théorie classique pour affirmer un parallèle entre densités conformes à la Patterson-Sullivan et densités harmoniques, et notamment définir une frontière de Martin où les densités ergodiques forment la partie minimale, et enfin l’identifier géométriquement sous hypothèse d’hyperbolicité.

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