Learn More
Similar sublattices of the root lattice A4 are possible [9] for each index that is the square of a non-zero integer of the form m 2 + mn − n 2. Here, we add a constructive approach, based on the arithmetic of the quaternion algebra H(Q (√ 5)) and the existence of a particular involution of the second kind, which also provides the actual sublattices and the(More)
Learning is but an adjunct to ourself And where we are our learning likewise is. Abstract The paper studies ways in which the sets of a partition of a lattice in R n become regular model sets. The main theorem gives equivalent conditions which assure that a matrix substitution system on a lattice in R n gives rise to regular model sets (based on p-adic-like(More)
The paper is about methods of discrete Fourier analysis in the context of Weyl group symmetry. Three families of class functions are defined on the maximal torus of each compact simply connected semisimple Lie group G. Such functions can always be restricted without loss of information to a fundamental regioň F of the affine Weyl group. The members of each(More)
Model sets (or cut and project sets) provide a familiar and commonly used method of constructing and studying nonperiodic point sets. Here we extend this method to situations where the internal spaces are no longer Euclidean, but instead spaces with p-adic topologies or even with mixed Euclidean/p-adic topologies. We show that a number of well known tilings(More)