T-tetrominoes tiling's Markov chain mixes fast

Korn and Pak (2007) [3] conjectured that there exists a fully polynomial randomized approximation scheme (fpras) for approximating the number of ways of tiling a 4n×4m rectangular lattice with T-tetrominoes. Using a flow argument, we prove this conjecture in affirmative by showing that the mixing time of an appropriate Markov chain is polynomial in the area of the lattice.