A184051 T(n,k) is the number of order-decreasing partial isometries (of an n-chain) with exactly k fixed points.

1, 1, 1, 2, 2, 1, 5, 4, 3, 1, 13, 6, 6, 4, 1, 30, 10, 10, 10, 5, 1, 66, 14, 15, 20, 15, 6, 1, 137, 22, 21, 35, 35, 21, 7, 1

Offset: 0

Author

Abdullahi Umar, Jan 12 2011

Keywords

• nonn
• easy
• tabl

Examples

			T (4,2) = 6 because there are exactly 6 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
		

Links

• R. Kehinde, S. O. Makanjuola and A. Umar, On the semigroup of order-decreasing partial isometries of a finite chain, arXiv:1101.2558

Crossrefs

Row sums are A184052 for n >= 0

Formula

T(n,0)= A184052(n) and T(n,k)=C(n,k), (k>0)