On Counting the Number of Tilings of a Rectangle with Squares of Size 1 and 2
نویسنده
چکیده
We consider tilings of a rectangle of size n×k with square tiles of size 1×1 and 2×2. We present a method to calculate the number of such tilings via matrix multiplication, where we optimize the number of multiplications needed and reduce the space required for the matrix multiplication by dynamically generating the matrices involved.
منابع مشابه
On the number of tilings of the rectangular board with T-tetronimoes
The classical combinatorial problem of counting domino tilings of a 2n × 2m rectangle was solved by P.W. Kasteleyn and also by H.N.V. Temperley and M.E. Fisher in 1961. We shall consider the similar problem for T-tetrominoes, that is, pieces formed by 4 unit squares in the shape of a T. We give explicit formulae for the number of tilings with T-tetrominoes for the 4n × 4m rectangle when n = 1, ...
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تاریخ انتشار 2016