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Permutations

# Permutations - CSE 1400 Applied Discrete Mathematics...

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Unformatted text preview: CSE 1400 Applied Discrete Mathematics Permutations Department of Computer Sciences College of Engineering Florida Tech Fall 2011 Permutations 1 Cyclic Notation 2 Permutations Re-Order a Sequence 2 Stirling Numbers of the First Kind 2 Problems on Permutations 4 Abstract A permutation is a one-to-one function from a set onto itself. Permutations A permutation is a function that rearranges the order of terms in a sequence . It is useful to study a few small examples. In computing practice, sorting a group of objects into a preferred order is a fundamental operation. Sorting algorithms perform a sequence of permutations on the objects, each bringing them closer to the preferred order. Consider the suits in a deck of playing cards: clubs ♣ , diamonds ♦ , hearts ♥ , and spades ♠ . There are 2! = 2 permutations of two things . ♣ ♦ ♣ ♥♦ ♣ ♦♥ ♣ ♣ ♦♥ ♣ ♦ ♥ ♣ ♦ ♣ ♥♦ ♣ ♦♥ There are 3! = 6 permutations of three things . Starting with a ♣ , after picking up a ♦ , place it before or after the ♣ . If you next draw a ♥ it can be place before, in the middle, or after the already permuted pairs. Imagine inserting a ♠ into one of the already arranged suits, say ♥ ♣ ♦ . There are four places where the ♠ can be inserted: first, sec- ond, third, or fourth. Reasoning like this it is not difficult to observe ♠ ♥ ♣ ♦ , ♥ ♠♣ ♦ , ♥ ♣♠ ♦ , ♥ ♣ ♦ ♠ there are 4! = 4 · 6 = 4 · 3 · 2 · 1 = 24 cse 1400 applied discrete mathematics...
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Permutations - CSE 1400 Applied Discrete Mathematics...

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