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The sequence whose definition is: "t is the first, fourth, eleventh, ... letter of this sentence." The first few values are 1, 4, 11, 16, 24, 29, 33, 35, 39, ... (OEIS ...

In general, an arrangement of objects is simply a grouping of them. The number of "arrangements" of n items is given either by a combination (order is ignored) or permutation ...

Arrow's paradox, also called Arrow's impossibility theorem or the general possibility theorem, states that perfect democratic voting is impossible, not just in practice but ...

An Artin L-function over the rationals Q encodes in a generating function information about how an irreducible monic polynomial over Z factors when reduced modulo each prime. ...

A module that fulfils the descending chain condition with respect to inclusion, i.e., if every decreasing sequence of submodules eventually become constant.

A general reciprocity theorem for all orders which covered all other known reciprocity theorems when proved by E. Artin in 1927. If R is a number field and R^' a finite ...

A series is called artistic if every three consecutive terms have a common three-way ratio P[a_i,a_(i+1),a_(i+2)]=((a_i+a_(i+1)+a_(i+2))a_(i+1))/(a_ia_(i+2)). A series is ...

Suppose that E(G) (the commuting product of all components of G) is simple and G contains a semisimple group involution. Then there is some semisimple group involution x such ...

Let p be an odd prime, a be a positive number such that pa (i.e., p does not divide a), and let x be one of the numbers 1, 2, 3, ..., p-1. Then there is a unique x^', called ...

Given a group action G×F->F and a principal bundle pi:A->M, the associated fiber bundle on M is pi^~:A×F/G->M. (1) In particular, it is the quotient space A×F/G where ...