Lecture-4 | Permutation | Maths Book | Tamil

Equality of two permutations: TWO permutations f and g of degree n are said to equal it we havef(a)=g(a) for every a belongs to s. ************************************************* Identity permutation: If l is a permutation of degree n such that I replaces each elenment by thee element itself, I is called the identity permutation of degree n. ******************************************************** Inverse permutation: An inverse permutation is a permutation in which each number and the number of the place which it occupies are exchanged. ******************************************************** Cyclic permutation: A permutation is called a cyclic permutation if and only if it has a single nontrivial cycle ( a cycle of length & greater than l). **************************************************** Even and odd permutations: A permutation is said to be an even permutation if it can be expressed as a product of an even no. of transpositions, otherwise it is said to be an odd permutation. ie it has an odd no.of transpositions. ******************************************************* Product or composite of two permutations: The product or composite of two permutations f and g of degree n denoted by fg is obtained by first carrying.