A111776 Triangle read by rows: number of idempotent order-preserving partial transformations (of an n-element chain) of waist k (waist(alpha) = max(Im(alpha))).

1, 1, 1, 1, 2, 3, 1, 4, 6, 10, 1, 8, 12, 20, 35, 1, 16, 24, 40, 70, 125, 1, 32, 48, 80, 140, 250, 450, 1, 64, 96, 160, 280, 500, 900, 1625

Offset

0,5

Comments

G(n, n) is A081567(n - 1)

References

Laradji, A. and Umar, A. Combinatorial results for semigroups of order-preserving partial transformations. Journal of Algebra 278, (2004), 342-359.

Links

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

Formula

G(n,k)= (2^(n-k))*G(n,n)=(2^(n-k))*A081567(n-1), G(0,0) = 1

Example

G(3,2) = 6 because there are exactly 6 idempotent order-preserving partial transformations (on a 3-element chain) of waist 2, namely: (2)->(2), (1,2)->(1,2), (1,2)->(2,2),(1,3)->(3,3), (2,3)->(2,2), (2,3)->(3,3) - the mappings are coordinate-wise

Crossrefs

Cf. A081567.

Sequence in context: A303648 A298364 A356769 * A189187 A299714 A171083

Adjacent sequences: A111773 A111774 A111775 * A111777 A111778 A111779

Keyword

nonn,tabl

Author

Abdullahi Umar, Aug 25 2008

Status

approved