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The Sierpiński carpet is the fractal illustrated above which may be constructed analogously to the Sierpiński sieve, but using squares instead of triangles. It can be ...

Let the sum of squares function r_k(n) denote the number of representations of n by k squares, then the summatory function of r_2(k)/k has the asymptotic expansion ...

As proved by Sierpiński (1960), there exist infinitely many positive odd numbers k such that k·2^n+1 is composite for every n>=1. Numbers k with this property are called ...

The silver constant is the algebraic number given by S = (x^3-5x^2+6x-1)_3 (1) = 2+2cos(2/7pi) (2) = 3.246979603... (3) (OEIS A116425), where (P(x))_n denotes a polynomial ...

A simple directed graph is a directed graph having no multiple edges or graph loops (corresponding to a binary adjacency matrix with 0s on the diagonal). The number of simple ...

A simple graph, also called a strict graph (Tutte 1998, p. 2), is an unweighted, undirected graph containing no graph loops or multiple edges (Gibbons 1985, p. 2; West 2000, ...

A simple polyhedron, also called a simplicial polyhedron, is a polyhedron that is topologically equivalent to a sphere (i.e., if it were inflated, it would produce a sphere) ...

The simplex method is a method for solving problems in linear programming. This method, invented by George Dantzig in 1947, tests adjacent vertices of the feasible set (which ...

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...

A siteswap is a sequence encountered in juggling in which each term is a positive integer, encoded in binary. The transition rule from one term to the next consists of ...