|
Search: id:A111776
|
|
|
| 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)). |
|
+0
3
|
|
| 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
(list; table; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
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.
|
|
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: A046671 A129566 A073809 this_sequence A021436 A118800 A075297
Adjacent sequences: A111773 A111774 A111775 this_sequence A111777 A111778 A111779
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
A. Umar (aumarh(AT)squ.edu.om), Aug 25 2008
|
|
|
Search completed in 0.002 seconds
|
