We describe a number of recently developed cluster-flipping algorithms for the efficient stimulation of classical spin models near their critical temperature. These include the algorithms of Wolff, Swendsen and Wang, and Niedermeyer, as well as the limited cluster algorithm, the multigrid...

We calculate the generating functions for the number of tilings of rectangles of various widths by the right tromino, the L tetromino, and the T tetromino. This allows us to place lower bounds on the entropy of tilings of the plane by each of these. For the T tetromino, we also derive a lower...