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The determination of the number of alternating permutations having elements {1,2,...,n}.

On an oriented n-dimensional Riemannian manifold, the Hodge star is a linear function which converts alternating differential k-forms to alternating (n-k)-forms. If w is an ...

The shoelace formula, also known as Gauss's area formula, the shoelace algorithm, shoelace method, or surveyor's formula, is a name sometimes given to the polygon area ...

An even alternating permutation number, more commonly called a tangent number.

An odd alternating permutation number, more commonly called an Euler number or secant number.

1 0 1 0 1 1 0 1 2 2 0 2 4 5 5 (1) The Entringer numbers E(n,k) (OEIS A008281) are the number of permutations of {1,2,...,n+1}, starting with k+1, which, after initially ...

The secant numbers S_k, also called the zig numbers or the Euler numbers E_n^*=|E_(2n)| numbers than can be defined either in terms of a generating function given as the ...

In mathematics, a knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the ...

Some authors define a general Airy differential equation as y^('')+/-k^2xy=0. (1) This equation can be solved by series solution using the expansions y = ...

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate ...