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

0,4

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

Example

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

Crossrefs

Row sums are A000325 for n >= 0

Sequence in context: A088333 A016538 A134226 * A367094 A324798 A226059

Adjacent sequences: A184047 A184048 A184049 * A184051 A184052 A184053

Keyword

nonn,tabl

Author

Abdullahi Umar, Jan 12 2011

Status

approved