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An arc-transitive graph, sometimes also called a flag-transitive graph, is a graph whose graph automorphism group acts transitively on its graph arcs (Godsil and Royle 2001, ...

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all ...

In its original form, the Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) S^3, ...

A nonplanar graph is a graph that is not planar. The numbers of simple nonplanar graphs on n=1, 2, ... nodes are 0, 0, 0, 0, 1, 14, 222, 5380, 194815, ... (OEIS A145269), ...

The orchard-planting problem (also known as the orchard problem or tree-planting problem) asks that n trees be planted so that there will be r(n,k) straight rows with k trees ...

The complexity c_n of an integer n is the least number of 1s needed to represent it using only additions, multiplications, and parentheses. For example, the numbers 1 through ...

Hilbert's problems are a set of (originally) unsolved problems in mathematics proposed by Hilbert. Of the 23 total appearing in the printed address, ten were actually ...

An n×n Latin square is a Latin rectangle with k=n. Specifically, a Latin square consists of n sets of the numbers 1 to n arranged in such a way that no orthogonal (row or ...

A regular continued fraction is a simple continued fraction x = b_0+1/(b_1+1/(b_2+1/(b_3+...))) (1) = K_(k=1)^(infty)1/(b_k) (2) = [b_0;b_1,b_2,...], (3) where b_0 is an ...

The so-called explicit formula psi(x)=x-sum_(rho)(x^rho)/rho-ln(2pi)-1/2ln(1-x^(-2)) gives an explicit relation between prime numbers and Riemann zeta function zeros for x>1 ...