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A Latin square is said to be reduced (also, normalized or in standard form) if both its first row and its first column are in their natural order. [4] For example, the Latin square above is not reduced because its first column is A, C, B rather than A, B, C. Any Latin square can be reduced by permuting (that is, reordering) the rows and columns ...
Latin squares and finite quasigroups are equivalent mathematical objects, although the former has a combinatorial nature while the latter is more algebraic.The listing below will consider the examples of some very small orders, which is the side length of the square, or the number of elements in the equivalent quasigroup.
A Graeco-Latin square or Euler square or pair of orthogonal Latin squares of order n over two sets S and T (which may be the same), each consisting of n symbols, is an n × n arrangement of cells, each cell containing an ordered pair (s, t), where s is in S and t is in T, such that every row and every column contains each element of S and each element of T exactly once, and that no two cells ...
When k = 1, that is, there is only one row, since the Latin rectangles are normalized there is no choice for what this row can be. The table also shows that L(n − 1, n) = L(n, n), which follows since if only one row is missing, the missing entry in each column can be determined from the Latin square property and the rectangle can be uniquely extended to a Latin square.
The minimum number of transversals of a Latin square is also an open problem. H. J. Ryser conjectured (Oberwolfach, 1967) that every Latin square of odd order has one. Closely related is the conjecture, attributed to Richard Brualdi, that every Latin square of order n has a partial transversal of order at least n − 1.
The most common superscript digits (1, 2, and 3) were included in ISO-8859-1 and were therefore carried over into those code points in the Latin-1 range of Unicode. The remainder were placed along with basic arithmetical symbols, and later some Latin subscripts, in a dedicated block at U+2070 to U+209F. The table below shows these characters ...
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The term Latin alphabet may refer to either the alphabet used to write Latin (as described in this article) or other alphabets based on the Latin script, which is the basic set of letters common to the various alphabets descended from the classical Latin alphabet, such as the English alphabet.