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The power polynomials x^n are an associated Sheffer sequence with f(t)=t, (1) giving generating function sum_(k=0)^inftyx^kt^k=1/(1-tx) (2) and exponential generating ...

A random composition of a number n in k parts is one of the (n+k-1; n) possible compositions of n, where (n; k) is a binomial coefficient. A random composition can be given ...

A function whose range is in the real numbers is said to be a real function, also called a real-valued function.

The Reeb foliation of the hypersphere S^3 is a foliation constructed as the union of two solid tori with common boundary.

A function is termed regular iff it is analytic and single-valued throughout a region R.

|_n]={n for n!=0; 1 for n=0. (1)

The m×n rook complement graph K_m square K_n^_ is the graph complement of the m×n rook graph. It has vertex count mn and edge count 2(m; 2)(n; 2), where (n; k) is a binomial ...

The period for a quasiperiodic trajectory to pass through the same point in a surface of section. If the rotation number is irrational, the trajectory will densely fill out a ...

Let R+B be the number of monochromatic forced triangles (where R and B are the number of red and blue triangles) in an extremal graph. Then R+B=(n; 3)-|_1/2n|_1/4(n-1)^2_|_|, ...

The second Morley cubic is the triangle cubic with trilinear equation It passes through Kimberling centers X_n for n=1, 1134, 1135, 1136, and 1137.