The linear-affine functional equation and group actions. Publications, to be read On the general solution of the system of cocycle equations without regularity conditions Tiling problems in music theory.

Tiling problems in music theory.

In G. Mazzola, Th. Noll, and E. Lluis-Puebla, editors, Perspectives in Mathematical and Computational Music Theory, pages 153-168. epOs Music, Osnabrück, 2004.

Abstract: In mathematical music theory we often come across various constructions on Zn , the set of residues modulo n for n > =2 . Different objects constructed on Zn are considered to be equivalent if there exists a symmetry motivated by music which transforms one object into the other one. Usually we are dealing with cyclic, dihedral, or affine symmetry groups on Zn . Here we will compare partitions of Zn , sometimes also called mosaics, and rhythmic tiling canons on Zn . Especially we will investigate regular complementary canons of maximal category in more details.

harald.fripertinger "at" uni-graz.at, February 2, 2010

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