Nonperiodicity implies unique composition for self-similar translationally finite Tilings

Let be a translationally finite self-similar tiling of R ^d . We prove that if is nonperiodic, then it has the unique composition property. More generally, has the unique composition property modulo the group of its translation symmetries. <lsiheader> <onlinepub>7 August, 1998 <editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; <pdfname>20n2p265.pdf <pdfexist>yes <htmlexist>no <htmlfexist>no <texexist>no <sectionname> </lsiheader> Received August 7, 1996, and in revised form December 18, 1996.