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A set of n magic circles is a numbering of the intersections of the n circles such that the sum over all intersections is the same constant for all circles. The above sets of ...

A set of n distinct numbers taken from the interval [1,n^2] form a magic series if their sum is the nth magic constant M_n=1/2n(n^2+1) (Kraitchik 1942, p. 143). The numbers ...

Let A_n be the set of all sequences that contain all sequences {a_k}_(k=0)^n where a_0=1 and all other a_i=+/-1, and define c_k=sum_(j=0)^(n-k)a_ja_(j+k). Then the merit ...

Let any finite or infinite set of points having no finite limit point be prescribed and associate with each of its points a principal part, i.e., a rational function of the ...

The direct sum of modules A and B is the module A direct sum B={a direct sum b|a in A,b in B}, (1) where all algebraic operations are defined componentwise. In particular, ...

The length of all composition series of a module M. According to the Jordan-Hölder theorem for modules, if M has any composition series, then all such series are equivalent. ...

The theorem of Möbius tetrads, also simply called Möbius's theorem by Baker (1925, p. 18), may be stated as follows. Let P_1, P_2, P_3, and P_4 be four arbitrary points in a ...

A monotonic matrix of order n is an n×n matrix in which every element is either 0 or contains a number from the set {1,...,n} subject to the conditions 1. The filled-in ...

A square-shaped neighborhood that can be used to define a set of cells surrounding a given cell (x_0,y_0) that may affect the evolution of a two-dimensional cellular ...

Given a sequence {a_i}_(i=1)^N, an n-moving average is a new sequence {s_i}_(i=1)^(N-n+1) defined from the a_i by taking the arithmetic mean of subsequences of n terms, ...