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The modern definition of the q-hypergeometric function is _rphi_s[alpha_1,alpha_2,...,alpha_r; beta_1,...,beta_s;q,z] ...

There are a great many beautiful identities involving q-series, some of which follow directly by taking the q-analog of standard combinatorial identities, e.g., the ...

A (-1,1)-matrix is a matrix whose elements consist only of the numbers -1 or 1. For an n×n (-1,1)-matrix, the largest possible determinants (Hadamard's maximum determinant ...

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 ...

The 11-cell is a regular 4-dimensional structure that cannot be represented in 3-dimensional space in any reasonable way and is highly self-intersecting even in 4-dimensional ...

A 30-60-90 triangle is a right triangle having angles of 30 degrees, 60 degrees, and 90 degrees. For a 30-60-90 triangle with hypotenuse of length a, the legs have lengths b ...

The triangle with edge lengths 3, 4, and 5 is the right triangle with smallest possible integer lengths and corresponds to the Pythagorean triple (3,4,5) where the legs have ...

How can a delegation of six regiments, each of which sends a colonel, a lieutenant-colonel, a major, a captain, a lieutenant, and a sub-lieutenant be arranged in a regular ...

The 57-cell, also called the pentacontaheptachoron, is a regular self-dual locally projective polytope with 57 hemidodecahedral facets described by Coxeter (1982) and also ...

The coordinate system obtained by inversion of Cartesian coordinates, with u,v,w in (-infty,infty). The transformation equations are x = u/(u^2+v^2+w^2) (1) y = ...