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An inverse permutation is a permutation in which each number and the number of the place which it occupies are exchanged. For example, p_1 = {3,8,5,10,9,4,6,1,7,2} (1) p_2 = ...

In determinant expansion by minors, the minimal number of transpositions of adjacent columns in a square matrix needed to turn the matrix representing a permutation of ...

An iterated map is a map that is applied repeatedly to an object. The Wolfram Language function NestList[f, expr, n] gives a list of the results of iterating the function f n ...

The Janko-Kharaghani-Tonchev graph is a strongly regular graph on 324 vertices and 24786 edges. It has regular parameters (nu,k,lambda,mu)=(324,153,72,72). It is implemented ...

The Janko-Kharaghani graphs are two strongly regular graph on 936 and 1800 vertices. They have regular parameters (nu,k,lambda,mu)=(936,375,150,150) and (1800,1029,588,588), ...

The problem of determining how many nonattacking kings can be placed on an n×n chessboard. For n=8, the solution is 16, as illustrated above (Madachy 1979). In general, the ...

Let phi_x^((k)) denote the recursive function of k variables with Gödel number x, where (1) is normally omitted. Then if g is a partial recursive function, there exists an ...

A theorem, also called the iteration theorem, that makes use of the lambda notation introduced by Church. Let phi_x^((k)) denote the recursive function of k variables with ...

A theorem which plays a fundamental role in computer science because it is one of the main tools for showing that certain orderings on trees are well-founded. These orderings ...

For every positive integer n, there exists a sphere which has exactly n lattice points on its surface. The sphere is given by the equation ...