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The binomial transform takes the sequence a_0, a_1, a_2, ... to the sequence b_0, b_1, b_2, ... via the transformation b_n=sum_(k=0)^n(-1)^(n-k)(n; k)a_k. The inverse ...

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 ...

Polynomials s_k(x;lambda) which form a Sheffer sequence with g(t) = 1+e^(lambdat) (1) f(t) = e^t-1 (2) and have generating function ...

The maximum number of regions that can be created by n cuts using space division by planes, cube division by planes, cylinder cutting, etc., is given by N_(max)=1/6(n^3+5n+6) ...

The nth central fibonomial coefficient is defined as [2n; n]_F = product_(k=1)^(n)(F_(n+k))/(F_k) (1) = ...

For every p, the kernel of partial_p:C_p->C_(p-1) is called the group of cycles, Z_p={c in C_p:partial(c)=0}. (1) The letter Z is short for the German word for cycle, ...

The number of ways to arrange n distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is P_n=(n-1)!. The number is (n-1)! instead ...

The compact-open topology is a common topology used on function spaces. Suppose X and Y are topological spaces and C(X,Y) is the set of continuous maps from f:X->Y. The ...

A metric space X which is not complete has a Cauchy sequence which does not converge. The completion of X is obtained by adding the limits to the Cauchy sequences. For ...

Let a graph G=(V,E) be defined on vertex set V and edge set E. Then a construction sequence (or c-sequence) for G is a linear order on V union E in which each edge appears ...