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

0,4

Links

Table of n, a(n) for n=0..35.

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

Formula

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

Example

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

Crossrefs

Row sums are A184052 for n >= 0

Sequence in context: A353738 A127742 A110438 * A121460 A105292 A273342

Adjacent sequences: A184048 A184049 A184050 * A184052 A184053 A184054

Keyword

nonn,easy,tabl

Author

Abdullahi Umar, Jan 12 2011

Status

approved