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In the field of percolation theory, the term percolation threshold is used to denote the probability which "marks the arrival" (Grimmett 1999) of an infinite connected ...

A planar straight line embedding of a planar graph is a planar embedding in which only straight line segments are used to connect the graph vertices. Fáry (1948) showed that ...

A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator ...

Let a number n be written in binary as n=(epsilon_kepsilon_(k-1)...epsilon_1epsilon_0)_2, (1) and define b_n=sum_(i=0)^(k-1)epsilon_iepsilon_(i+1) (2) as the number of digits ...

A series-reduced tree is a tree in which all nodes have degree other than 2 (in other words, no node merely allows a single edge to "pass through"). Series-reduced trees are ...

An integer is k-smooth if it has no prime factors >k. The following table gives the first few k-smooth numbers for small k. Berndt (1994, p. 52) called the 7-smooth numbers ...

Square line picking is the selection of pairs of points (corresponding to endpoints of a line segment) randomly placed inside a square. n random line segments can be picked ...

Stirling's approximation gives an approximate value for the factorial function n! or the gamma function Gamma(n) for n>>1. The approximation can most simply be derived for n ...

The mean tetrahedron volume of a tetrahedron with vertices chosen at random inside another tetrahedron of unit volume is given by V^_ = (13)/(720)-(pi^2)/(15015) (1) = ...

Let L be a nontrivial bounded lattice (or a nontrivial complemented lattice, etc.). If every nonconstant lattice homomorphism defined on L is 0,1-separating, then L is a ...