Generalized balanced pair algorithms for substitution tiling spaces
by
Brian F. Martensen
University of Texas at Austin
Coauthors: Lorenzo Sadun

For substitution tiling spaces, the ``balanced pair" algorithm is a convenient way to determine if the substitutive system has pure point spectrum. Unfortunately, this algorithm does not always terminate, though is known to work fairly well in constant length or irreducible cases. In this talk, we examine various generalizations of this algorithm. We see what additional cases these generalizations now handle and examine the consequences on determining the spectrum on fairly general systems.

Date received: February 28, 2003