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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 ...

An (n,k)-banana tree, as defined by Chen et al. (1997), is a graph obtained by connecting one leaf of each of n copies of an k-star graph with a single root vertex that is ...

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

A Barker code is a string of digits a_i=+/-1 of length l>=2 such that |sum_(i=1)^(l-k)a_ia_(i+k)|<=1 for all 1<=k<l. Barker codes are used for pulse compression of radar ...

A number defined by b_n=b_n(0), where b_n(x) is a Bernoulli polynomial of the second kind (Roman 1984, p. 294), also called Cauchy numbers of the first kind. The first few ...

11 21 3 41 4 7 81 5 11 15 161 6 16 26 31 32 (1) The number triangle illustrated above (OEIS A008949) composed of the partial sums of binomial coefficients, a_(nk) = ...

Bertelsen's number is an erroneous name erroneously given to the erroneous value of pi(10^9)=50847478, where pi(x) is the prime counting function. This value is 56 lower than ...

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 ...

A bicolorable graph G is a graph with chromatic number chi(G)<=2. A graph is bicolorable iff it has no odd graph cycles (König 1950, p. 170; Skiena 1990, p. 213; Harary 1994, ...