generate t-combinations of a set
Combination(n, t, opts)
nonnegint; size of set
nonnegint; size of combinations
(optional) equation(s) of the form option = value; specify options for the Combination command
compile = truefalse
True means compile the iterator. The default is true.
rank = nonnegint
Specify the starting rank of the iterator. The default is one. Passing a value greater than one causes the iterator to skip the lower ranks; this can be useful when parallelizing iterators. The starting rank reverts to one when the iterator is reset, reused, or copied.
The Combination command returns an iterator that generates all t-combinations of the integers 0..n−1.
The combinations, when read from right to left, appear in lexicographic order.
The n parameter is the size of the set.
The t parameter is the number of elements in each combination.
If n<t, the iterator generates nothing.
If n=t=0, the iterator generates a single empty Array.
In addition to the common iterator methods, this iterator object has the following methods. The self parameter is the iterator object.
Number(self): return the number of iterations required to step through the iterator, assuming it started at rank one.
Rank(self,L): return the rank of the current iteration. Optionally pass L, a list or one-dimensional rtable, and return its rank.
Unrank(self,rnk): return a one-dimensional Array corresponding to the iterator output with rank rnk.
Construct an iterator that returns all 3-combinations of the integers from 0 to 4.
n,t ≔ 5,3:
M ≔ Combination⁡n,t:
1: 0 1 2
2: 0 1 3
3: 0 2 3
4: 1 2 3
5: 0 1 4
6: 0 2 4
7: 1 2 4
8: 0 3 4
9: 1 3 4
10: 2 3 4
Compute the number of iterations.
Return the element with rank equal to 4.
Copy the iterator, but start with rank equal to 4.
N ≔ Object⁡M,'rank'=4:
Knuth, Donald Ervin. The Art of Computer Programming, volume 4, fascicle 3; generating all combinations and partitions, sec. 188.8.131.52, algorithm T (Lexicographic combinations), p. 5.
The Iterator[Combination] command was introduced in Maple 2016.
For more information on Maple 2016 changes, see Updates in Maple 2016.
The Iterator[Combination] command was updated in Maple 2022.
The n and t parameters were updated in Maple 2022.
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