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Search: id:A110858
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| A110858 |
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Triangle read by rows: number of order-preserving partial transformations (of an n-element chain) of width and waist both equal to r (width(alpha) = |Dom(alpha)| and waist(alpha) = max(Im(alpha)). |
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+0
1
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| 1, 1, 1, 1, 2, 2, 1, 3, 6, 6, 1, 4, 12, 24, 20, 1, 5, 20, 60, 100, 70, 1, 6, 30, 120, 300, 420, 252, 1, 7, 42, 210, 700, 1470, 1764, 924
(list; table; graph; listen)
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OFFSET
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1,5
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REFERENCES
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Laradji, A. and Umar, A. Combinatorial results for semigroups of order-preserving partial transformations. Journal of Algebra 278, (2004), 342-359
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FORMULA
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G(n,k)=C(n,k)*C(2*k-2,k-1), n >=k >0
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EXAMPLE
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G(3,2)=6 because there are exactly 6 order-preserving partial transformations (on a 3-element chain) of both width and waist equal to 2, namely: (1,2)->(1,2),(1,2)->(2,2),(1,3)->(1,2),(1,3)->(2,2),(2,3)->(1,2),(2,3)->(2,2)
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CROSSREFS
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Sequence in context: A107111 A082037 A163649 this_sequence A008279 A056043 A158497
Adjacent sequences: A110855 A110856 A110857 this_sequence A110859 A110860 A110861
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KEYWORD
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nonn,tabl
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AUTHOR
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A. Umar (aumarh(AT)squ.edu.om), Aug 25 2008
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