If you are a graduate student and would like to participate in the poster session, please send by email your title, affiliation and full abstract (approximately 100-150 words) NO LATER THAN JUNE 10th to:
William A. MasseyThe poster session will be held the evening of Wednesday, JUNE 26 at Bell Laboratories (Lucent Technologies, Murray Hill). Materials such as poster boards, push pins, tape, etc. will be provided there. You only need to bring the mathematics (exposition, formulas, and graphs). We look forward to seeing you this summer!!
E-mail: will@research.att.com
Phone: 908-582-3225
Nathaniel Dean, AT&T Research (nate@research.att.com)
William A. Massey, Bell Laboratories (will@research.att.com)
A POLYOMINO TILING PROBLEM OF THURSTON AND ITS CONFIGURATIONAL ENTROPY
Terry Gauss Newton
Department of Mathematics
University of Hilbert Space
xyz@hilbert.space.edu
We prove a conjecture of Thurston on tiling a certain triangular region $T_{3N+1}$ of the hexagonal lattice with three-in-line (``tribone'') tiles. It asserts that for all packings of $T_{3N+1}$ with tribones leaving exactly one uncovered cell, the uncovered cell must be the central cell. Furthermore, there are exactly $2^{N}$ such packings. This exact counting result is analogous to closed formulae for the number of allowable configurations in certain exactly solved models in statistical mechanics, and implies that the configurational entropy (per site) of tiling $T_{3N+1}$ with tribones with one defect tends to 0 as $N \rightarrow \infty$.