Call Us Now: 8185279935

Call Us Now: 8185279935

Home » Math Homework Help » Algebra Homework Help » Permutation Function |

Permutation Function

In this section we shall give the definition and some properties of permutation function which are useful in the development of the theory of determinants.

Inversion

Let

x |
P_{1}(x) |
P_{2}(x) |
P_{3}(x) |
P_{4}(x) |
P_{5}(x) |
P_{6}(x) |

1 | 1 | 1 | 2 | 2 | 3 | 3 |

2 | 2 | 3 | 1 | 3 | 1 | 2 |

3 | 3 | 2 | 3 | 1 | 2 | 1 |

No. of inversion |
0 | 1 | 1 | 2 | 2 | 3 |

Value of δ(p) |
+ | — | — | + | + | |

terms |
(a_{11} a_{22} a_{33}) |
(—a_{11} a_{23} a_{31}) |
(—a_{11} a_{21} a_{32}) |
(a_{12} a_{21} a_{32}) |
(a_{13} a_{21} a_{31}) |
(—a_{13} a_{22} a_{31}) |

**Definition:**A one-one function whose domain and the range is the same set, the set being finite, is called a permutation function. For example, let**S = {1, 2, 3}**be a finite set, then there are**3 ! = 6**permutation functions**p**defined from_{1}, p_{2}, p_{3}, p_{4}, p_{5}, p_{6}**S**to**S**. Let us explain the permutation functions by means of the above table.Inversion

Let

**p**be a permutation function and**i < j**be a pair of elements in its domain such that**p (i) > p (j)**, then p is said to have an inversion. For example if**S = {1, 2}**and the permutation function is**p**_{2}, then we notice from the above table that**2 < i p(2) > p(1)**and as such**p**_{2}has one inversion. Obviously,**p**_{1}has zero inversion. In other words, an inversion is said to take place if in a permutation**3, 1 and 2**, we have the couples**(1, 2)**which gives one inversion.**Services: -**Permutation Function Homework | Permutation Function Homework Help | Permutation Function Homework Help Services | Live Permutation Function Homework Help | Permutation Function Homework Tutors | Online Permutation Function Homework Help | Permutation Function Tutors | Online Permutation Function Tutors | Permutation Function Homework Services | Permutation FunctionSubmit Your Query ???

Assignment Help

Calculus Homework Help
Algebra Homework Help
Abstract Algebra Help
Discrete Math Help
Topics

Real Number Absolute Value
Addition Of Matrices
Square Matrix Adjoint
Algebraic Structures
Alternating Series
Linear Equations Determinants
Archimedean Real Numbers
Binary Operation
Binary Relation In A Set
Bounded, Unbounded Sets
Cauchy Root Test
Caylay Hamiltion Theorem
Circular Permutation
Common Roots
Complex Numbers
Complex Number Conjugate
Conjugate Of A Matrix
Constant Sequences
Convergence Of A Sequence
Cosets
Cubic, Biquadratic Equations
De Moivre Theorem
Real Number Denseness
Order 3 Determinants
Differences Of Matrices
Direct Sum Of Vector Subspaces
Eigen Vector
Elementary Matrices
Matrix Elem. Transformations
Equal Matrices
Equal Roots
Two Permutations Equity
Equivalent Matrices
Trigonometry Function Expansion
Field
Function
Algebra Fundamental Theorem
Gaussian Integer
Geometric Series
Group
Ideals
Quantity Increasing Roots
Infinite Series Convergent
Integers
Inverse Of Square Matrix
Inverses Of Elementary Matrices
Iota, Imaginary Numbers
Left-Right Identity
Sequence Limit Points
Linear Combination Vectors Span
Linear Dependence, Independence
Linear Homogeneous Equations
Two Subspaces Linear Sum
Matric Polynomial
Matrix
Linear Equation Matrix Inverse
Matrix Multiplication
Matrix Scalar Multiplication
Method Of Difference
Minors And Co-factors
Multiplication Modulo P
Normal Sub-Group
Normalizer Or Centalizer
Orbit Of Permutation
Peano Axioms
Permutation Function
Pigeon Hole Principle
Matrices Integral Powers
Mathematical Induction Principal
Two Determinants Product
Two Permutations Product
Properties Of Modulus
Rank Of A Matrix
Rational Numbers
Rational, Integral Polynomial
Reciprocal Roots
Relation Of Sets
Rings Of A Set
Row By Column Matrix
Sequence
Series
Series Of Positive Terms
Series Partial Sum Sequence
Subrings
Sum Of A Series
Cosine Series Sum
Sum Of Sine Series
Symmetric/Skew Symm. Matrices
Roots Symmetric Functions
Symmetric Set Degree N
Synthetic Division
Transformation In General
Transformations Of Equations
Transpose Of A Matrix
Matrix Transposed Conjugate
Transposition
Complex Numbers Representation
Vector Space
Vector Sub-spaces
Whole Numbers
To book a free session write to:- tutoring@thehomeworkhelp.co.uk or call 8185279935