Use bijections to show that the number of permutations in S, avoiding the pattern 231 equals the number of permutations in these sets: 1. The set of 132-avoiding permutations, denoted Sn (132), which are charac- terized by having no indices i

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
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Problem 108.
Use bijections to show that the number of permutations in Sn avoiding the
pattern 231 equals the number of permutations in these sets:
1. The set of 132-avoiding permutations, denoted Sn (132), which are charac-
terized by having no indices i < j<k with w(i) <w(k) <w(j).
2. The set of 213-avoiding permutations, denoted Sn (213), which are charac-
terized by having no indices i < j<k with w(j) <w(i) <w(k).
3. The set of 312-avoiding permutations, denoted Sn (312), which are charac-
terized by having no indices i<j<k with w(j) <w(k) <w(i).
Transcribed Image Text:Problem 108. Use bijections to show that the number of permutations in Sn avoiding the pattern 231 equals the number of permutations in these sets: 1. The set of 132-avoiding permutations, denoted Sn (132), which are charac- terized by having no indices i < j<k with w(i) <w(k) <w(j). 2. The set of 213-avoiding permutations, denoted Sn (213), which are charac- terized by having no indices i < j<k with w(j) <w(i) <w(k). 3. The set of 312-avoiding permutations, denoted Sn (312), which are charac- terized by having no indices i<j<k with w(j) <w(k) <w(i).
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