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The Krohn-Rhodes complexity, also called the group complexity or simply "the complexity," of a finite semigroup S is the smallest number of groups in a wreath product of ...

Let a graph G have exactly 2n-3 graph edges, where n is the number of graph vertices in G. Then G is "generically" rigid in R^2 iff e^'<=2n^'-3 for every subgraph of G having ...

A branch point whose neighborhood of values wrap around an infinite number of times as their complex arguments are varied. The point z=0 under the function lnz is therefore a ...

A magic hexagram is a hexagram partitioned into triangles such that the sums of numbers in the six directions illustrated above sum to the same number. There are exactly two ...

A set-like object in which order is ignored, but multiplicity is explicitly significant. Therefore, multisets {1,2,3} and {2,1,3} are equivalent, but {1,1,2,3} and {1,2,3} ...

The letter O is used for a number of different purposes in mathematics. The double-struck O is sometimes used to represent octonions. The symbols O(x) (sometimes called the ...

An algebraic surface of degree eight. The maximum number of ordinary double points known to exist on an octic surface is 168 (the Endraß octics), although the rigorous upper ...

Let A be a set. An operation on A is a function from a power of A into A. More precisely, given an ordinal number alpha, a function from A^alpha into A is an alpha-ary ...

A surface which is homeomorphic to a finite collection of spheres, each with a finite number of handles, cross-handles, cross-caps, and perforations. A preliminary version of ...

Let f(z) be an analytic function in an angular domain W:|argz|<alphapi/2. Suppose there is a constant M such that for each epsilon>0, each finite boundary point has a ...