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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 ...

First stated in 1924, the Banach-Tarski paradox states that it is possible to decompose a ball into six pieces which can be reassembled by rigid motions to form two balls of ...

A column-convex self-avoiding polygon which contains the bottom edge of its minimal bounding rectangle. The anisotropic perimeter and area generating function ...

The Barth decic is a decic surface in complex three-dimensional projective space having the maximum possible number of ordinary double points, namely 345. It is given by the ...

The Barth sextic is a sextic surface in complex three-dimensional projective space having the maximum possible number of ordinary double points, namely 65. The surface was ...

When the index nu is real, the functions J_nu(z), J_nu^'(z), Y_nu(z), and Y_nu^'(z) each have an infinite number of real zeros, all of which are simple with the possible ...

The biggest little polygon with n sides is the convex plane n-gon of unit polygon diameter having largest possible area. Reinhardt (1922) showed that for n odd, the regular ...

The binary logarithm log_2x is the logarithm to base 2. The notation lgx is sometimes used to denote this function in number theoretic literature. However, because Russian ...

There are several related series that are known as the binomial series. The most general is (x+a)^nu=sum_(k=0)^infty(nu; k)x^ka^(nu-k), (1) where (nu; k) is a binomial ...

Bit rate (i.e., bits per second, abbreviated bps) is a measure of the number of data bits (digital 0s and 1s) transmitted each second in a digital communications channel. If ...