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The set of sums sum_(x)a_xx ranging over a multiplicative group and a_i are elements of a field with all but a finite number of a_i=0. Group rings are graded algebras.

A relation between permutations p and q that exists if there is a sequence of transpositions such that each transposition increases the number of inversions (Stanton and ...

The number of elements greater than i to the left of i in a permutation gives the ith element of the inversion vector (Skiena 1990, p. 27).

The Labs septic is a septic surface having 99 ordinary double points, which is the maximum number known for any septic surface.

Data resulting from the observation of a population on a number of variables over time. Whenever observations are made more than once, the data is considered to be ...

A Maurer rose is a plot of a "walk" along an n- (or 2n-) leafed rose curve in steps of a fixed number d degrees, including all cosets.

Let R be a number ring of degree n with 2s imaginary embeddings. Then every ideal class of R contains an ideal J such that ||J||<=(n!)/(n^n)(4/pi)^ssqrt(|disc(R)|), where ...

The permutohedron is the n-dimensional generalization of the hexagon. The n-permutohedron is the convex hull of all permutations of the vector (x_1,x_2,...,x_(n+1)) in ...

A function or curve is piecewise continuous if it is continuous on all but a finite number of points at which certain matching conditions are sometimes required.

An algebraic extension K over a field F is a purely inseparable extension if the algebraic number minimal polynomial of any element has only one root, possibly with ...