Bookcover of Parity of a Permutation
Booktitle:

Parity of a Permutation

Betascript Publishing (2010-06-06 )

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ISBN-13:

978-613-0-33564-9

ISBN-10:
6130335644
EAN:
9786130335649
Book language:
English
Blurb/Shorttext:
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, when X is a finite set of at least two elements, the permutations of X (i.e. the bijective mappings from X to X) fall into two classes of equal size: the even permutations and the odd permutations. If any total ordering of X is fixed, the parity (oddness or evenness) of a permutation σ of X can be defined as the parity of the number of inversions for σ, i.e., of pairs of elements x,y of X such that x < y and σ(x) > σ(y). The sign or signature of a permutation σ is denoted sgn(σ) and defined as +1 if σ is even and −1 if σ is odd. The signature defines the alternating character of the symmetric group Sn. Another notation for the sign of a permutation is given by the more general Levi-Civita symbol (εσ), which is defined for all maps from X to X, and has value zero for non-bijective maps.
Publishing house:
Betascript Publishing
Website:
https://www.betascript-publishing.com/
Edited by:
Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
Number of pages:
84
Published at:
2010-06-06
Stock:
Available
Category:
Mathematics
Price:
34.00 €
Keywords:
Mathematics, Finite Set, Permutation, Total Order, Symmetric Group, Transposition (mathematics), Function Composition, Group Homomorphism, Alternating Group, Length Function

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