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The sum over all external (square) nodes of the lengths of the paths from the root of an extended binary tree to each node. For example, in the tree above, the external path ...

The study of how the intrinsic structure of graphs ensures certain types of properties (e.g., clique-formation and graph colorings) under appropriate conditions.

Let X be a set and S a collection of subsets of X. A set function mu:S->[0,infty] is said to possess finite monotonicity provided that, whenever a set E in S is covered by a ...

A finitely presented group is a group with a finite number of generators and relations. A mathematical joke involving finitely presented groups is given by Renteln and Dundes ...

Special functions which arise as solutions to second order ordinary differential equations are commonly said to be "of the first kind" if they are nonsingular at the origin, ...

The first Napoleon point N, also called the outer Napoleon point, is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of ...

An object created by folding a piece of paper along certain lines to form loops. The number of states possible in an n-flexagon is a Catalan number. By manipulating the ...

An (n,k) fountain is an arrangement of n coins in rows such that exactly k coins are in the bottom row and each coin in the (i+1)st row touches exactly two in the ith row. ...

Let (x_1,x_2) and (y_1,y_2) be two sets of complex numbers linearly independent over the rationals. Then the four exponential conjecture posits that at least one of ...

The maximum possible weight of a fractional clique of a graph G is called the fractional clique number of G, denoted omega^*(G) (Godsil and Royle 2001, pp. 136-137) or ...