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The ring of integers of a number field K, denoted O_K, is the set of algebraic integers in K, which is a ring of dimension d over Z, where d is the extension degree of K over ...

The series with sum sum_(n=0)^infty1/(F_(2^n))=1/2(7-sqrt(5)), where F_k is a Fibonacci number (Honsberger 1985).

Let R be a number ring of degree n with 2s imaginary embeddings. Then every ideal class of R contains an ideal J such that ||J||<=(n!)/(n^n)(4/pi)^ssqrt(|disc(R)|), where ...

The operation of subtraction, i.e., a minus b. The operation is denoted a-b. The minus sign "-" is also used to denote a negative number, i.e., -x.

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

A number n is k-multiperfect (also called a k-multiply perfect number or k-pluperfect number) if sigma(n)=kn for some integer k>2, where sigma(n) is the divisor function. The ...

A graph or directed graph together with a function which assigns a positive real number to each edge (Harary 1994, p. 52).

An odd number is an integer of the form n=2k+1, where k is an integer. The odd numbers are therefore ..., -3, -1, 1, 3, 5, 7, ... (OEIS A005408), which are also the gnomonic ...

The path covering number (or path-covering number; Slater 1972) of a graph G, variously denoted as summarized below, is the minimum number of vertex-disjoint paths that cover ...

The permutohedron is the n-dimensional generalization of the hexagon. The n-permutohedron is the convex hull of all permutations of the vector (x_1,x_2,...,x_(n+1)) in ...