Search Results for ""

A trivalent tree, also called a 3-valent tree or a 3-Cayley tree, is a tree for which each node has vertex degree <=3. The numbers of trivalent trees on n=1, 2, ... nodes are ...

Find the m×n array of single digits which contains the maximum possible number of primes, where allowable primes may lie along any horizontal, vertical, or diagonal line. For ...

The inverse trigonometric functions are the inverse functions of the trigonometric functions, written cos^(-1)z, cot^(-1)z, csc^(-1)z, sec^(-1)z, sin^(-1)z, and tan^(-1)z. ...

Orthogonal polynomials are classes of polynomials {p_n(x)} defined over a range [a,b] that obey an orthogonality relation int_a^bw(x)p_m(x)p_n(x)dx=delta_(mn)c_n, (1) where ...

A tiling of regular polygons (in two dimensions), polyhedra (three dimensions), or polytopes (n dimensions) is called a tessellation. Tessellations can be specified using a ...

The truncated icosahedron is the 32-faced Archimedean solid with 60 vertices corresponding to the facial arrangement 20{6}+12{5}. It is also the uniform polyhedron with ...

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 ...

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 ...