Unformatted text preview: plication tables match up as well; see Exercise 1.5.2 . Notice that the order in which permutations are multiplied matters in general. For example, ± 1 2 3 2 1 3 ²± 1 2 3 2 3 1 ² D ± 1 2 3 1 3 2 ² ; but ± 1 2 3 2 3 1 ²± 1 2 3 2 1 3 ² D ± 1 2 3 3 2 1 ² : For any natural number n , the permutations of n identical objects can be denoted by twoline arrays of numbers, containing the numbers 1 through n in each row. If a permutation ± moves an object from position i to position j , then the corresponding two line array has j positioned below i . The numbers in the ﬁrst row are generally arranged in increasing order, but this is not essential. Permutations are multiplied or composed according to the same rule as given previously for permutations of three objects. For example, we have the following product of permutations of seven objects:...
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 Fall '08
 EVERAGE
 Algebra, Permutations, Multiplication, Position, multiplication table

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