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Fuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in ...

The Hadwiger number of a graph G, variously denoted eta(G) (Zelinka 1976, Ivančo 1988) or h(G) (Stiebitz 1990), is the number of vertices in the largest complete minor of G ...

The Pierce expansion, or alternated Egyptian product, of a real number 0<x<1 is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

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 ...

The Sobolev embedding theorem is a result in functional analysis which proves that certain Sobolev spaces W^(k,p)(Omega) can be embedded in various spaces including ...

Let X be a set of v>=3 elements together with a set B of 3-subset (triples) of X such that every 2-subset of X occurs in exactly one triple of B. Then B is called a Steiner ...

The wallpaper groups are the 17 possible plane symmetry groups. They are commonly represented using Hermann-Mauguin-like symbols or in orbifold notation (Zwillinger 1995, p. ...

The Farey sequence F_n for any positive integer n is the set of irreducible rational numbers a/b with 0<=a<=b<=n and (a,b)=1 arranged in increasing order. The first few are ...

The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...

Let S(x) denote the number of positive integers not exceeding x which can be expressed as a sum of two squares (i.e., those n<=x such that the sum of squares function ...