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A nilpotent Lie group is a Lie group G which is connected and whose Lie algebra is a nilpotent Lie algebra g. That is, its Lie algebra lower central series ...

Polykites are polyforms obtained from a regular triangular grid superposed on a regular hexagonal grid (its dual), illustrated above. The monokite is therefore a ...

A polyhedron having two polygons in parallel planes as bases and triangular or trapezoidal lateral faces with one side lying in one base and the opposite polyhedron vertex or ...

A statistic w on the symmetric group S_n is called a weighted inversion statistic if there exists an upper triangular matrix W=(w_(ij)) such that ...

Let the difference of successive primes be defined by d_n=p_(n+1)-p_n, and d_n^k by d_n^k={d_n for k=1; |d_(n+1)^(k-1)-d_n^(k-1)| for k>1. (1) N. L. Gilbreath claimed that ...

There are a number of attractive compounds of two regular tetrahedra. The most symmetrical is the arrangement whose outer hull is the stella octangula (left figure), while ...

Archimedes' cattle problem, also called the bovinum problema, or Archimedes' reverse, is stated as follows: "The sun god had a herd of cattle consisting of bulls and cows, ...

The complete bipartite graph K_(1,3) is a tree known as the "claw." It is isomorphic to the star graph S_4, and is sometimes known as the Y graph (Horton and Bouwer 1991; ...

In 1803, Malfatti posed the problem of determining the three circular columns of marble of possibly different sizes which, when carved out of a right triangular prism, would ...

The Fritsch graph is the 9-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...