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A square matrix with constant skew diagonals. In other words, a Hankel matrix is a matrix in which the (i,j)th entry depends only on the sum i+j. Such matrices are sometimes ...

For an n×n matrix, let S denote any permutation e_1, e_2, ..., e_n of the set of numbers 1, 2, ..., n, and let chi^((lambda))(S) be the character of the symmetric group ...

An algebraic loop L is a Moufang loop if all triples of elements x, y, and z in L satisfy the Moufang identities, i.e., if 1. z(x(zy))=((zx)z)y, 2. x(z(yz))=((xz)y)z, 3. ...

Attractive compounds of four octahedra can be constructed as the duals of the cube 4-compounds. These compounds will be implemented in a future version of the Wolfram ...

One would think that by analogy with the matching-generating polynomial, independence polynomial, etc., a path polynomial whose coefficients are the numbers of paths of ...

The semiperimeter on a figure is defined as s=1/2p, (1) where p is the perimeter. The semiperimeter of polygons appears in unexpected ways in the computation of their areas. ...

A transformation that preserves angles and changes all distances in the same ratio, called the ratio of magnification. A similarity can also be defined as a transformation ...

Given a set of n men and n women, marry them off in pairs after each man has ranked the women in order of preference from 1 to n, {w_1,...,w_n} and each women has done ...

Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y, (2) where x·y is vector multiplication which is assumed to be bilinear. Now define ...

Let h:{0,1}^(l(n))×{0,1}^n->{0,1}^(m(n)) be efficiently computable by an algorithm (solving a P-problem). For fixed y in {0,1}^(l(n)), view h(x,y) as a function h_y(x) of x ...