- Bookcover of Parity of a Permutation
- Booktitle:
-
Parity of a Permutation
Betascript Publishing (2010-06-06 )
eligible for voucher
- ISBN-13:
978-613-0-33564-9
- ISBN-10:
- 6130335644
- EAN:
- 9786130335649
- Book language:
- 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
