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Search: id:A145034
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| A145034 |
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T(n,k) is the number of order-decreasing and order-preserving partial transformations (of an n-chain) of width (width(alpha) = |Dom(alpha)|) and waist (waist(alpha) = max(Im(alpha))) both equal to k. |
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1
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| 1, 1, 1, 1, 2, 1, 3, 4, 2, 1, 4, 9, 12, 5, 1, 5, 16, 36, 40, 14, 1, 6, 25, 80, 150, 140, 42, 1, 7, 36, 150, 400, 630, 504, 132
(list; table; graph; listen)
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OFFSET
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0,5
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REFERENCES
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Laradji, A. and Umar, A. Combinatorial results for semigroups of order-decreasing partial transformations. J. Integer Seq. 7, (2004), 04.3.8, 14 pp.
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LINKS
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Laradji, A. and Umar, A. Combinatorial Results for Semigroups of Order-Decreasing Partial Transformations , Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.8. [From A. Umar (aumarh(AT)squ.edu.om), Oct 07 2008]
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FORMULA
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T(n,k)=C(n,k)C(2k-2,k-1)(n-k+1)/n, (n>=k>=1), T(n,0)=1
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EXAMPLE
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T(3,2) = 4 because there are exactly 4 order-decreasing and order-preserving partial transformations (of a 3-chain) of width and waist both equal to 2, namely: (1,2)->(1,2), (1,3)->(1,2), (2,3)->(1,2), (2,3)->(2,2).
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CROSSREFS
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Sequence in context: A106382 A004741 A133923 this_sequence A125158 A112384 A123390
Adjacent sequences: A145031 A145032 A145033 this_sequence A145035 A145036 A145037
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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), Sep 30 2008
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