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Consider an infinite repository containing balls of n different types. Then the following table summarizes the number of distinct ways in which k balls can be picked for four ...

A braid index is the least number of strings needed to make a closed braid representation of a link. The braid index is equal to the least number of Seifert circles in any ...

The second part of Pollard rho factorization method concerns detection of the fact that a sequence has become periodic. Pollard's original suggestion was to use the idea ...

A notation used to describe curves. The fundamental principle of Clebsch-Aronhold notation states that if each of a number of forms be replaced by a power of a linear form in ...

Combinatorial matrix theory is a rich branch of mathematics that combines combinatorics, graph theory, and linear algebra. It includes the theory of matrices with prescribed ...

Some computations allow shortcuts which can be used to speed them up. Consider the operation of raising a number to a positive integer power. It is possible, for example, to ...

Let C be a smooth geometrically connected projective curve over F_q with q=p^s a prime power. Let infty be a fixed closed point of X but not necessarily F_q-rational. A ...

The even part Ev(n) of a positive integer n is defined by Ev(n)=2^(b(n)), where b(n) is the exponent of the exact power of 2 dividing n. The values for n=1, 2, ..., are 1, 2, ...

There are two important theorems known as Herbrand's theorem. The first arises in ring theory. Let an ideal class be in A if it contains an ideal whose lth power is ...

Let [a_0;a_1,a_2,...] be the simple continued fraction of a "generic" real number, where the numbers a_i are the partial quotients. Then the Khinchin (or Khintchine) harmonic ...