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Let S be a set of n+1 symbols, then a Howell design H(s,2n) on symbol set S is an s×s array H such that 1. Every cell of H is either empty or contains an unordered pair of ...

Two objects form a mirror pair if one can be translated and rotated in such a way that the two objects together possess mirror symmetry, i.e., one is the mirror image of the ...

Montgomery's pair correlation conjecture, published in 1973, asserts that the two-point correlation function R_2(r) for the zeros of the Riemann zeta function zeta(z) on the ...

Given any set B, the associated pair groupoid is the set B×B with the maps alpha(a,b)=a and beta(a,b)=b, and multiplication (a,b)·(b,c)=(a,c). The inverse is ...

The axiom of Zermelo-Fraenkel set theory which asserts the existence for any sets a and b of a set x having a and b as its only elements. x is called the unordered pair of a ...

Bicentric perspective is the study of the projection of 3D space from a pair of fiducial points instead of a single one, the latter of which may be called "centric" or ...

A roll of 10 on a pair of six-sided dice in the game of craps (Gardner 1978, p. 256). The probability of rolling "a big Dick" is 1/12, or 8.333...%.

An ordered pair (a,b) of nonnegative integers such that there is some set of a points and b edges whose removal disconnects the graph and there is no set of a-1 nodes and b ...

An arc of a graph, sometimes also called a flag, is an ordered pair of adjacent vertices (Godsil and Royle 2001, p. 59), sometimes also called a directed line (Harary 1994, ...

If a graph G has n graph vertices such that every pair of the n graph vertices which are not joined by a graph edge has a sum of valences which is >=n, then G is Hamiltonian. ...