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Dominos can tile the plane in a countably infinite number of ways. The number of tilings of a 2×n rectangle with dominoes is , the nth Fibonacci number. [5]Domino tilings figure in several celebrated problems, including the Aztec diamond problem in which large diamond-shaped regions have a number of tilings equal to a power of two, [6] with most tilings appearing random within a central ...
Any non-simple members of each family are listed, as well as any members duplicated within a family or between families. (In removing duplicates it is useful to note that no two finite simple groups have the same order, except that the group A 8 = A 3 (2) and A 2 (4) both have order 20160, and that the group B n ( q ) has the same order as C n ...
Muggins is part of the Fives family of domino games whose names differ according to how many spinners are in play. Muggins is the game without a spinner, Sniff and modern All Fives have a single spinner, and, in Five Up, all doubles are spinners. [2] However, historically Fives or All Fives was the progenitor of the family and had no spinners. [3]
Dominoes is a family of tile-based games played with gaming pieces. Each domino is a rectangular tile, usually with a line dividing its face into two square ends. Each end is marked with a number of spots (also called pips or dots) or is blank. The backs of the tiles in a set are indistinguishable, either blank or having some common design.
The name domino for the game piece is believed to come from the spotted masquerade garment domino, from Latin dominus. [58] Despite this word origin, in naming polyominoes, the first letter d- of domino is fancifully interpreted as a version of the prefix di- meaning "two", and replaced by other numerical prefixes .
The mutilated chessboard problem is an instance of domino tiling of grids and polyominoes, also known as "dimer models", a general class of problems whose study in statistical mechanics dates to the work of Ralph H. Fowler and George Stanley Rushbrooke in 1937. [1]
In geometry, a domino tiling of a region in the Euclidean plane is a tessellation of the region by dominoes, shapes formed by the union of two unit squares meeting edge-to-edge. Equivalently, it is a perfect matching in the grid graph formed by placing a vertex at the center of each square of the region and connecting two vertices when they ...
In mathematics, the classification of finite simple groups (popularly called the enormous theorem [1] [2]) is a result of group theory stating that every finite simple group is either cyclic, or alternating, or belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six exceptions, called sporadic (the Tits group is sometimes regarded as a sporadic group ...
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