generate t-combinations of a set
Combination(n, t, opts)
posint; 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. 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; it must be less than or equal to n.
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.
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.
Knuth, Donald Ervin. The Art of Computer Programming, volume 4, fascicle 3; generating all combinations and partitions, sec. 184.108.40.206, 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.
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