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The term pairwise refers to taking all unordered 2-subsets of a given set. For example, the pairwise products of the set {a,b,c} are ab, ac, and bc.

The knot move obtained by fixing disk 1 in the figure above and flipping disks 2 and 3.

A group of four elements, also called a quadruplet or tetrad.

A group of three elements, also called a triad. A triple is therefore a 3-tuple.

An aliquot sequence computed using the analog of the restricted divisor function s^*(n) in which only unitary divisors are included.

Differential Geometry

Roughly speaking, isospectral manifolds are drums that sound the same, i.e., have the same eigenfrequency spectrum. Two drums with differing area, perimeter, or genus can ...

Given a general quadratic curve Ax^2+Bxy+Cy^2+Dx+Ey+F=0, (1) the quantity X is known as the discriminant, where X=B^2-4AC, (2) and is invariant under rotation. Using the ...

Two nonisomorphic graphs that have equal resistance spectra (i.e., multisets of resistance distances) are said to be resistance-equivalent. All nonisomorphic simple graphs on ...

A divisor d of n for which GCD(d,n/d)=1, (1) where GCD(m,n) is the greatest common divisor. For example, the divisors of 12 are {1,2,3,4,6,12}, so the unitary divisors are ...