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Given a linear code C of length n and dimension k over the field F, a parity check matrix H of C is a n×(n-k) matrix whose rows generate the orthogonal complement of C, i.e., ...

A groupoid S such that for all a,b in S, there exist unique x,y in S such that ax = b (1) ya = b. (2) No other restrictions are applied; thus a quasigroup need not have an ...

A sorting algorithm which makes n passes over a set of n elements, in each pass selecting the smallest element and deleting it from the set. This algorithm has running time ...

A partially ordered set is defined as an ordered pair P=(X,<=). Here, X is called the ground set of P and <= is the partial order of P.

A relation "<=" is called a preorder (or quasiorder) on a set S if it satisfies: 1. Reflexivity: a<=a for all a in S. 2. Transitivity: a<=b and b<=c implies a<=c. A preorder ...

For x>0, J_0(x) = 2/piint_0^inftysin(xcosht)dt (1) Y_0(x) = -2/piint_0^inftycos(xcosht)dt, (2) where J_0(x) is a zeroth order Bessel function of the first kind and Y_0(x) is ...

There are no tilings of the equilateral triangle of side length 7 by all the polyhexes of order n=4. There are nine distinct solutions of all the polyhexes of order n=4 which ...

C_4 is one of the two groups of group order 4. Like C_2×C_2, it is Abelian, but unlike C_2×C_2, it is a cyclic. Examples include the point groups C_4 (note that the same ...

A square which is magic under multiplication instead of addition (the operation used to define a conventional magic square) is called a multiplication magic square. Unlike ...

For some authors (e.g., Bourbaki, 1964), the same as principal ideal domain. Most authors, however, do not require the ring to be an integral domain, and define a principal ...