Geodesic
Some equinumerous pattern-avoiding classes of permutations
Discrete mathematics & theoretical computer science, Tome 7 (2005).

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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 α β γ where |α |=r, |γ |=s and β is any arrangement of \1,2,\ldots,p\∪ \m-q+1, m-q+2, \ldots,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.\par 2000 MATHEMATICS SUBJECT CLASSIFICATION: 05A05 
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     author = {Atkinson, M. D.},
     title = {Some equinumerous pattern-avoiding classes of permutations},
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Atkinson, M. D. Some equinumerous pattern-avoiding classes of permutations. Discrete mathematics & theoretical computer science, Tome 7 (2005). doi : 10.46298/dmtcs.356. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.356/

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