-ordered set partitions.
combinat::splitNK is a low level combinatorial class for -ordered set partitions.
Categories
Cat::CombinatorialClass, Cat::FacadeDomain(DOM_LIST)
See Also:
combinat::chooseNK, combinat::multisetsNK, combinat::permutationsNK
Details:
A 
-set partition is an ordered set partition of 
into two subsets of respective sizes 
and 
. It is represented by a pair of two sorted lists.
This is a fast low-level combinatorial class, with a simplistic interface by design.
count – number of fenced(k,n-k)-set partitions
combinat::splitNK::count(nonnegative integer 
, nonnegative integer 
)
Returns the number of 
-set partitions.
generator – generator for the fenced(k,n-k)-set partitions
combinat::splitNK::generator(nonnegative integer 
, nonnegative integer 
)
Returns a generator for the 
-set partitions in lexicographic order.
list – list of the fenced(k,n-k)-set partitions
combinat::splitNK::list(nonnegative integer 
, nonnegative integer 
)
Returns the list of all the 
-set partitions in lexicographic order.
random – random fenced(k,n-k)-set partition
combinat::splitNK::random(nonnegative integer 
, nonnegative integer 
)
Returns a random 
-set partition.
Here is the list of all the 
-set partitions. This gives all the ways to split the set 
into one subset of size 
and one of size 
:
combinat::splitNK::list(5,2)
Changes in MuPAD 4.0
New Function.