Some equinumerous pattern-avoiding classes of permutations
Suppose that p,q,r,s are non-negative integers with m=p+q+r+s. The class X(p,q,r,s) of permutations that contain no pattern of the form αβγ where |α|=r, |γ|=s and β is any arrangement of {1,2,…,p}∪{m-q+1, m-q+2, …,m} is considered. A recurrence relation to enumerate the permutations of X(...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2005-12-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Online Access: | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/62 |
| Summary: | Suppose that p,q,r,s are non-negative integers with m=p+q+r+s. The class X(p,q,r,s) of permutations that contain no pattern of the form αβγ where |α|=r, |γ|=s and β is any arrangement of {1,2,…,p}∪{m-q+1, m-q+2, …,m} is considered. A recurrence relation to enumerate the permutations of X(p,q,r,s) is established. The method of proof also shows that X(p,q,r,s)=X(p,q,1,0)X(1,0,r,s) in the sense of permutational composition. 2000 MATHEMATICS SUBJECT CLASSIFICATION: 05A05 |
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| ISSN: | 1462-7264 1365-8050 |