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In n dimensions for n>=5 the arrangement of hyperspheres whose convex hull has minimal content is always a "sausage" (a set of hyperspheres arranged with centers along a ...

A smooth function is a function that has continuous derivatives up to some desired order over some domain. A function can therefore be said to be smooth over a restricted ...

An integer n is called a super unitary perfect number if sigma^*(sigma^*(n))=2n, where sigma^*(n) is the unitary divisor function. The first few are 2, 9, 165, 238, 1640, ... ...

A number of attractive tetrahedron 10-compounds can be constructed. The first (left figures) can be obtained by combining tetrahedron 5-compounds of opposite chirality ...

A plane partition which is invariant under permutation of the three axes and which is equal to its complement (i.e., the collection of cubes that are in a given box but do ...

A trail is a walk v_0, e_1, v_1, ..., v_k with no repeated edge. The length of a trail is its number of edges. A u,v-trail is a trail with first vertex u and last vertex v, ...

The height of a tree g is defined as the vertex height of its root vertex, where the vertex height of a vertex v in a tree g is the number of edges on the longest downward ...

A brute-force method of finding a divisor of an integer n by simply plugging in one or a set of integers and seeing if they divide n. Repeated application of trial division ...

An ultrametric is a metric which satisfies the following strengthened version of the triangle inequality, d(x,z)<=max(d(x,y),d(y,z)) for all x,y,z. At least two of d(x,y), ...

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections ...