4204hw8 - π Conclude that the permutations that can be...

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Combinatorics II (MAD 4204) — Spring 2011 Due Wednesday 4/6/11 Homework #8 1 Which permutation is sorted by the stack word ssspssppppsp ? 2 Suppose that instead of sorting with a stack, we generate permutations with a stack. That is, we start with the identity on the right and pass it through a stack to generate a permutation π . Prove that π can be generated by a stack if and only if π 1 can be sorted with a stack. (Here π 1 denotes the group-theoretic inverse of
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Unformatted text preview: π .) Conclude that the permutations that can be generated by a stack are precisely the 312-avoiding permutations. 3 Using the terminology of the previous problem, which permutations can be generated with two parallel queues? 4 Prove that for every k , the permutation π avoids k 21 if and only if the entries of π can be partitioned into k 1 (possibly empty) increasing subse-quences....
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