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The Schröder number S_n is the number of lattice paths in the Cartesian plane that start at (0, 0), end at (n,n), contain no points above the line y=x, and are composed only ...

For an integer n>=2, let lpf(n) denote the least prime factor of n. A pair of integers (x,y) is called a twin peak if 1. x<y, 2. lpf(x)=lpf(y), 3. For all z, x<z<y implies ...

The Young tableau (plural, "tableaux") of a Ferrers diagram is obtained by placing the numbers 1, ..., n in the n boxes of the diagram. A "standard" Young tableau is a Young ...

The harmonic parameter of a polyhedron is the weighted mean of the distances d_i from a fixed interior point to the faces, where the weights are the areas A_i of the faces, ...

There are (at least) two mathematical constants associated with Theodorus. The first Theodorus's constant is the elementary algebraic number sqrt(3), i.e., the square root of ...

Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

A two-dimensional affine geometry constructed over a finite field. For a field F of size n, the affine plane consists of the set of points which are ordered pairs of elements ...

An algebraic equation in n variables is an polynomial equation of the form f(x_1,x_2,...,x_n)=sum_(e_1,...,e_n)c_(e_1,e_2,...,e_n)x_1^(e_1)x_2^(e_2)...x_n^(e_n)=0, where the ...

Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

Informally, the term asymptotic means approaching a value or curve arbitrarily closely (i.e., as some sort of limit is taken). A line or curve A that is asymptotic to given ...