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A double-toroidal graph is a graph with graph genus 2 (West 2000, p. 266). Planar and toroidal graphs are therefore not double-toroidal. Some known double-toroidal graphs on ...

A dissection of a rectangle into smaller rectangles such that the original rectangle is not divided into two subrectangles. Rectangle dissections into 3, 4, or 6 pieces ...

The following are equivalent definitions for a Galois extension field (also simply known as a Galois extension) K of F. 1. K is the splitting field for a collection of ...

Like the entire harmonic series, the harmonic series sum_(k=1)^infty1/(p_k)=infty (1) taken over all primes p_k also diverges, as first shown by Euler in 1737 (Nagell 1951, ...

The inverse tangent integral Ti_2(x) is defined in terms of the dilogarithm Li_2(x) by Li_2(ix)=1/4Li_2(-x^2)+iTi_2(x) (1) (Lewin 1958, p. 33). It has the series ...

Arrange copies of the n digits 1, ..., n such that there is one digit between the 1s, two digits between the 2s, etc. For example, the unique (modulo reversal) n=3 solution ...

A k-matching in a graph G is a set of k edges, no two of which have a vertex in common (i.e., an independent edge set of size k). Let Phi_k be the number of k-matchings of ...

Let G be a finite, connected, undirected graph with graph diameter d(G) and graph distance d(u,v) between vertices u and v. A radio labeling of a graph G is labeling using ...

A closed planar quadrilateral with opposite sides of equal lengths a and b, and with four right angles. A square is a degenerate rectangle with a=b. The area of the rectangle ...

The reversal of a positive integer abc...z is z...cba. The reversal of a positive integer n is implemented in the Wolfram Language as IntegerReverse[n]. A positive integer ...