A184050 T(n,k) is the number of order-preserving and order-decreasing partial isometries (of an n-chain) with exactly k fixed points.

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, 7, 21, 35, 35, 21, 7, 1

Offset: 0

Author

Abdullahi Umar, Jan 12 2011

Keywords

• nonn
• tabl

Examples

			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
		

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 A000325 for n >= 0

Formula

T(n,0)= A000325(n-1) and T(n,k)=C(n,k), (k>0)