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%I #9 Mar 31 2012 10:23:26
%S 1,1,1,2,2,1,5,3,3,1,12,4,6,4,1,27,5,10,10,5,1,58,6,15,20,15,6,1,121,
%T 7,21,35,35,21,7,1
%N T(n,k) is the number of order-preserving and order-decreasing partial isometries (of an n-chain) with exactly k fixed points.
%H R. Kehinde, S. O. Makanjuola and A. Umar, <a href="http://arxiv.org/abs/1101.2558">On the semigroup of order-decreasing partial isometries of a finite chain</a>, arXiv:1101.2558.
%F T(n,0)= A000325(n-1) and T(n,k)=C(n,k), (k>0)
%e T (4,2) = 6 because there are exactly 6 order-preserving and order-decreasing partial isometries (on a 4-chain) of fix 2, namely: (1,2)-->(1,2); (2,3)-->(2,3); (3,4)-->(3,4); (1,3)-->(1,3); (2,4)-->(2,4); (1,4)-->(1,4) - the mappings are coordinate-wise
%Y Row sums are A000325 for n >= 0
%K nonn,tabl
%O 0,4
%A _Abdullahi Umar_, Jan 12 2011
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