RestrictedPartitions( n, set )
RestrictedPartitions( n, set, k )
NrRestrictedPartitions( n, set )
NrRestrictedPartitions( n, set, k )
In the first form RestrictedPartitions returns the set of all
restricted partitions of the positive integer n with the summands of
the partition coming from the set set. In the second form
RestrictedPartitions returns the set of all partitions of the positive
integer n into sums with k summands with the summands of the
partition coming from the set set.
In the first form NrRestrictedPartitions returns the number of
restricted partitions of the positive integer n with the summands
coming from the set set. In the second form NrRestrictedPartitions
returns the number of restricted partitions of the positive integer n
into sums with k summands with the summands of the partition coming
from the set set.
A restricted partition is like an ordinary partition (see Partitions)
an unordered sum n = p_1+p_2 +..+ p_k of positive integers and is
represented by the list p = [p_1,p_2,..,p_k], in nonincreasing order.
The difference is that here the p_i must be elements from the set
set, while for ordinary partitions they may be elements from [1..n].
gap> RestrictedPartitions( 8, [1,3,5,7] );
[ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 3, 1, 1, 1, 1, 1 ], [ 3, 3, 1, 1 ],
[ 5, 1, 1, 1 ], [ 5, 3 ], [ 7, 1 ] ]
gap> NrRestrictedPartitions( 50, [1,5,10,25,50] );
50
The last example tells us that there are 50 ways to return 50 cent change using 1, 5, 10 cent coins, quarters and halfdollars.
GAP 3.4.4