Abstract: A polyiamond is an edge-connected set of cells on the planar triangular lattice. The area of a polyiamond is the number of cells it contains. The growth constant of polyiamonds, $\lambda_T$, is the limit of the ratio between the number of polyiamonds of area n+1 and the number of polyiamonds of area n, as n tends to infinity. In this talk I will show improved lower and upper bounds on $\lambda_T$, proving that it is between 2.8424 and 3.6050.
Joint work with Mira Shalah and Yufei Zheng (both from Technion, Israel).
Short bio sketch: Gill Barequet is currently an Associate Professor and Vice Dean for Curriculum at the Faculty of Computer Science of the Technion (Israel Institute of Technology) in Haifa, Israel. He received his B.Sc. in Mathematics and Computer Science, and M.Sc. and Ph.D. in Computer Science from Tel Aviv University in 1985, 1987, and 1994, respectively. He later had a post-doctoral position at Johns Hopkins University in 1996-98, and a visiting position at Tufts University in 2009-10. His research interests include discrete and computational geometry, combinatorics, and interpolation and reconstruction algorithms. He holds five U.S. patents in related areas.