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# Alternating permutation

In combinatorial mathematics, an alternating permutation (or zigzag permutation) of the set is an arrangement of those numbers so that each entry is alternately greater or less than the preceding entry. 

## Alternating group

In mathematics, an alternating group is the group of even permutations of a finite set.

## Asymptotic expansion

In mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular, often infinite, point.

## Bernoulli number

In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory.

## Bijection

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

## Boustrophedon transform

In mathematics, the boustrophedon transform is a procedure which maps one sequence to another.

## Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

## Catalan number

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects.

## Combinatorics

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.

## Comptes rendus de l'Académie des Sciences

Comptes rendus de l'Académie des Sciences (English: Proceedings of the Academy of sciences), or simply Comptes rendus, is a French scientific journal which has been published since 1666.

## Désiré André

Désiré André (André Antoine Désiré) (March 29, 1840, Lyon – September 12, 1917, Paris) was a French mathematician, best known for his work on Catalan numbers and alternating permutations.

## Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

## Empty set

In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

## Euler number

In mathematics, the Euler numbers are a sequence En of integers defined by the Taylor series expansion where is the hyperbolic cosine.

## Even and odd functions

In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses.

## Fence (mathematics)

In mathematics, a fence, also called a zigzag poset, is a partially ordered set in which the order relations form a path with alternating orientations: or A fence may be finite, or it may be formed by an infinite alternating sequence extending in both directions.

## Generating function

In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.

## Journal de Mathématiques Pures et Appliquées

The Journal de Mathématiques Pures et Appliquées is a French monthly scientific journal of mathematics, founded in 1836 by Joseph Liouville (editor: 1836–1874).

## Longest alternating subsequence

In combinatorial mathematics, probability, and computer science, in the longest alternating subsequence problem, one wants to find a subsequence of a given sequence in which the elements are in alternating order, and in which the sequence is as long as possible.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Partially ordered set

In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

## Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

## Radius of convergence

In mathematics, the radius of convergence of a power series is the radius of the largest disk in which the series converges.

## Richard P. Stanley

Richard Peter Stanley (born June 23, 1944 in New York City, New York) is the Norman Levinson Professor of Applied Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts.

## Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

## Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

## References

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