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A lattice polygon consisting of a closed self-avoiding walk on a square lattice. The perimeter, horizontal perimeter, vertical perimeter, and area are all well-defined for ...

A self-avoiding walk is a path from one point to another which never intersects itself. Such paths are usually considered to occur on lattices, so that steps are only allowed ...

Let the number of random walks on a d-D hypercubic lattice starting at the origin which never land on the same lattice point twice in n steps be denoted c_d(n). The first few ...

A self-complementary graph is a graph which is isomorphic to its graph complement. The numbers of simple self-complementary graphs on n=1, 2, ... nodes are 1, 0, 0, 1, 2, 0, ...

A partition whose conjugate partition is equivalent to itself. The Ferrers diagrams corresponding to the self-conjugate partitions for 3<=n<=10 are illustrated above. The ...

A point process N is called self-correcting if cov(N(s,t),N(t,u))<0 for s<t<u where here, cov denotes the covariance of the two quantities. Intuitively, a process is ...

The sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ... (OEIS A002024) consisting of 1 copy of 1, 2 copies of 2, 3 copies of 3, and so on. Surprisingly, there exist simple formulas ...

A 10-digit number satisfying the following property. Number the digits 0 to 9, and let digit n be the number of ns in the number. There is exactly one such number: 6210001000.

A number of areas of mathematics have the notion of a "dual" which can be applies to objects of that particular area. Whenever an object A has the property that it is equal ...

A self-dual graphs is a graph that is dual to itself. Wheel graphs are self-dual, as are the examples illustrated above. Naturally, the skeleton of a self-dual polyhedron is ...