|
Search: id:A144084
|
|
|
| A144084 |
|
T(n, k) is the number of partial bijections of height k (height(alpha) = |Im(alpha)|) of an n-element set. |
|
+0
1
|
|
| 1, 1, 1, 1, 4, 2, 1, 9, 18, 6, 1, 16, 72, 96, 24, 1, 25, 200, 600, 600, 120, 1, 36, 450, 2400, 5400, 4320, 720, 1, 49, 882, 7350, 29400, 52920, 35280, 5040
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
T(n,k) is also the number of elements in the Green's J equivalence classes in the symmetric inverse monoid, I sub n.
|
|
REFERENCES
|
Howie, J. M., Fundamentals of semigroup theory. Oxford: Clarendon Press, (1995).
Munn, W. D., The characters of the symmetric inverse semigroup. Proc. Cambridge Philos. Soc. 53 (1957), 13-18.
|
|
FORMULA
|
T(n,k)= (C(n,k)^2)*k!
|
|
EXAMPLE
|
T(3,1) = 9 because there are exactly 9 partial bijections (on a 3-element set) of height 1, namely: (1)->(1), (1)->(2), (1)->(3), (2)->(1), (2)->(2), (2)->(3), (3)->(1), (3)->(2), (3)->(3)
|
|
CROSSREFS
|
T(n, k) = |A021010|. Sum of rows of T(n, k) is A002720. T(n, n) is the order of the symmetric group on an n-element set, n!
Sequence in context: A101020 A160905 A063983 this_sequence A021010 A075397 A049429
Adjacent sequences: A144081 A144082 A144083 this_sequence A144085 A144086 A144087
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
A. Umar (aumarh(AT)squ.edu.om), Sep 10 2008, Sep 30 2008
|
|
|
Search completed in 0.002 seconds
|
