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Search: id:A111589
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| A111589 |
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Triangle read by rows: number of idempotent order-preserving partial transformations (of an n-element totally ordered set) of width k (width(alpha) = |Dom(alpha)| |
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+0
1
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| 1, 1, 1, 1, 2, 3, 1, 3, 9, 8, 1, 4, 18, 32, 21, 1, 5, 30, 80, 105, 55, 1, 6, 45, 160, 315, 330, 144, 1, 7, 63, 280, 735, 1155, 1008, 377
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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F(n; n) is A001906(n), n >= 1.
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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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F(n,k)= C(n,k)*A001906(k-1), (n>=k>0),F(0,0)=1
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EXAMPLE
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F(3,2) = 9 because there are exactly 9 idempotent order-preserving partial transformations (on a 3-element chain) of width 2, namely: (1,2)->(1,1), (1,2)->(1,2), (1,2)->(2,2), (1,2)->(3,3), (1,3)->(1,1), (1,3)->(1,3),(1,3)->(3,3), (2,3)->(2,2), (2,3)->(2,3),( 2,3)->(3,3) - the mappings are coordinate-wise
Triangle begins:
1,
1,1,
1,2,3,
1,3,9,8,
1,4,18,32,21,
1,5,30,80,105,55,
1,6,45,160,315,330,144, ...
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CROSSREFS
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Cf. A001906.
Sequence in context: A152440 A134319 A135091 this_sequence A010027 A151880 A108990
Adjacent sequences: A111586 A111587 A111588 this_sequence A111590 A111591 A111592
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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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EXTENSIONS
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Minor edits by N. J. A. Sloane (njas(AT)research.att.com), Jan 01 2009
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