Discrete Mathematics & Theoretical Computer Science, Vol 7 (2005)

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DMTCS vol 7 no 1 (2005), pp. 71-74

Discrete Mathematics & Theoretical Computer Science


Volume 7 n° 1 (2005), pp. 71-74

author:M. D. Atkinson
title:Some equinumerous pattern-avoiding classes of permutations
keywords:Permutations, patterns, enumeration
abstract: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.

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reference: M. D. Atkinson (2005), Some equinumerous pattern-avoiding classes of permutations, Discrete Mathematics and Theoretical Computer Science 7, pp. 71-74
bibtex:For a corresponding BibTeX entry, please consider our BibTeX-file.
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