Authors: Gill Barequet ¹; Micha Moffie ¹; Ares Ribó ²; Günter Rote ²

• 1 Department of Computer Science [Haifa]
• 2 Institut für Informatik [Berlin]

We improve the lower bounds on Klarner's constant, which describes the exponential growth rate of the number of polyominoes (connected subsets of grid squares) with a given number of squares. We achieve this by analyzing polyominoes on a different surface, a so-called $\textit{twisted cylinder}$ by the transfer matrix method. A bijective representation of the "states'' of partial solutions is crucial for allowing a compact representation of the successive iteration vectors for the transfer matrix method.