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The word "order" is used in a number of different ways in mathematics. Most commonly, it refers to the number of elements in (e.g., conjugacy class order, graph order, group ...

The index of a permutation p is defined as the sum of all subscripts j such that p_j>p_(j+1), for 1<=j<=n. MacMahon (1960) proved that the number of permutations of size n ...

A problem which is both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP-problem can be translated into this problem). Examples of NP-hard problems ...

The P versus NP problem is the determination of whether all NP-problems are actually P-problems. If P and NP are not equivalent, then the solution of NP-problems requires (in ...

A biquadratic number is a fourth power, n^4. The first few biquadratic numbers are 1, 16, 81, 256, 625, ... (OEIS A000583). The minimum number of biquadratic numbers needed ...

Let a_n and b_n be the perimeters of the circumscribed and inscribed n-gon and a_(2n) and b_(2n) the perimeters of the circumscribed and inscribed 2n-gon. Then a_(2n) = ...

The number of binary bits necessary to represent a number, given explicitly by BL(n) = 1+|_lgn_| (1) = [lg(n+1)], (2) where [x] is the ceiling function, |_x_| is the floor ...

Any computable function can be incorporated into a program using while-loops (i.e., "while something is true, do something else"). For-loops (which have a fixed iteration ...

An iterated map is a map that is applied repeatedly to an object. The Wolfram Language function NestList[f, expr, n] gives a list of the results of iterating the function f n ...

A formal structure for the organization of information. Examples of data structures include the list, queue, stack, and tree.