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Riddell's formula for unlabeled graphs is the Euler transform relating the number of unlabeled connected graphs on n nodes satisfying some property with the corresponding ...

The Robbins constant is the mean line segment length, i.e., the expected distance between two points chosen at random in cube line picking, namely Delta(3) = (1) = (2) = ...

The Robertson-Seymour theorem, also called the graph minor theorem, is a generalization of the Kuratowski reduction theorem by Robertson and Seymour, which states that the ...

The process of approximating a quantity, be it for convenience or, as in the case of numerical computations, of necessity. If rounding is performed on each of a series of ...

If the sides of a triangle are divided in the ratios lambda:1, mu:1, and nu:1, the cevians form a central triangle whose area is ...

A symbol of the form {p,q,r,...} used to describe regular polygons, polyhedra, and their higher-dimensional counterparts. The symbol {p} denotes a regular polygon for integer ...

A mathematical object defined for a set and a binary operator in which the multiplication operation is associative. No other restrictions are placed on a semigroup; thus a ...

A septic graph is a regular graph of degree seven. The numbers of (not necessarily connected) simple septic graphs on n=8, 10, 12, ... vertices are 1, 5, 1547, 21609301, ...

Consider the sum (1) where the x_js are nonnegative and the denominators are positive. Shapiro (1954) asked if f_n(x_1,x_2,...,x_n)>=1/2n (2) for all n. It turns out ...

Let the sum of squares function r_k(n) denote the number of representations of n by k squares, then the summatory function of r_2(k)/k has the asymptotic expansion ...