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Ramsey's theorem is a generalization of Dilworth's lemma which states for each pair of positive integers k and l there exists an integer R(k,l) (known as the Ramsey number) ...

It is possible to find six points in the plane, no three on a line and no four on a circle (i.e., none of which are collinear or concyclic), such that all the mutual ...

Pick two real numbers x and y at random in (0,1) with a uniform distribution. What is the probability P_(even) that [x/y], where [r] denotes the nearest integer function, is ...

A method of proof which proceeds by stating a proposition and then showing that it results in a contradiction, thus demonstrating the proposition to be false. In the words of ...

An idealized computing machine consisting of a fixed set of data registers and set of instructions for operating on them. Register machines are also known as counter machines ...

The Ricci flow equation is the evolution equation d/(dt)g_(ij)(t)=-2R_(ij) for a Riemannian metric g_(ij), where R_(ij) is the Ricci curvature tensor. Hamilton (1982) showed ...

There exist infinitely many odd integers k such that k·2^n-1 is composite for every n>=1. Numbers k with this property are called Riesel numbers, while analogous numbers with ...

Building on work of Huntington (1933ab), Robbins conjectured that the equations for a Robbins algebra, commutativity, associativity, and the Robbins axiom !(!(x v y) v !(x v ...

The conjecture that the equations for a Robbins algebra, commutativity, associativity, and the Robbins axiom !(!(x v y) v !(x v !y))=x, where !x denotes NOT and x v y denotes ...

A special graph vertex that is designated to turn a tree into a rooted tree or a graph into a rooted graph. The root is sometimes also called "eve," or an "endpoint" (Saaty ...