In his book [1], Solomon W. Golomb states that the problem of determining how many ways a 4 x n rectangle can be tiled by right trominoes "appears to be a challenging problem with reasonable hope of an attainable solution." This problem was solved in [5] by using generating functions, and similar results have been obtained in [6] by S Heubach, P Chinn, and P Callahan, who considered the problem of tiling rectangles with right and straight trominoes. Other beautiful results on right trominoes can be found in [2], [3], or [4]. In this article we present a matrix approach to the suggestion made by Golomb, which has the advantage of being applicable to arbitrary m x n rectangles-although it also has the drawback of using rather large matrices. The main result (see Theorem 1), though not especially difficult, seems to have passed unnoticed so far With the help of mathematical software packages such as Mathematica we are able to find, for example, the number of different tilings for squares of side a multiple of 3 up to the 12 x 12 case, as well as generating functions for the number of tilings of rectangles with right trominoes. We also state some results about the tilability of a family of regions called strips, which include rectangles as a particular case.
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机译：所罗门·W·戈洛姆布（Solomon W. Golomb）在他的书[1]中指出，确定一个4 x n矩形可以被正确的Tromino瓷砖平铺多少方法的问题“似乎是一个具有挑战性的问题，有合理的希望可以实现。”通过使用生成函数在[5]中解决了该问题，并且在[6]中S Heubach，P Chinn和P Callahan获得了类似的结果，他们考虑了平铺具有直角和直角Tromino的矩形的问题。可以在[2]，[3]或[4]中找到其他有关右Tromino的漂亮结果。在本文中，我们针对Golomb提出的建议提出了一种矩阵方法，该方法具有适用于任意m x n矩形的优点，尽管它也存在使用较大矩阵的缺点。主要结果（见定理1）尽管不是特别困难，但到目前为止似乎没有引起注意。借助数学软件包（如Mathematica），我们能够找到a边平方的不同平铺数目。 3的倍数，最高为12 x 12的情况，以及生成具有正确Tromino的矩形的平铺数量的函数。我们还陈述了有关称为条带的一系列区域的可使用性的一些结果，这些区域在特定情况下包括矩形。
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