On 21/02/2019 9:59, Jori Mäntysalo (TAU) wrote:
On Tue, 19 Feb 2019, TB wrote:
There is the cardinality method of IntegerVectors. Note that the default for
min_part is 0.
So this could be used for...?
I do not know the area. I was just playing with numbers (original question
was "In how many ways you can arrange a queue of 9 men and 7 women such
that no two women are next to each other?"), and noticed that
.cardinality() in sage/combinat/partition.py even has algorithm-parameter.
So I think there might be existing code just waiting for interface.
A composition can be thought as an integer vector with only natural
numbers. So theoretically Compositions() could have been implemented
using IntegerVectors(), which has a (buggy?) cardinality method that
does use binomials coefficients, and not just naive brute force. For
example:
sage: Compositions(10, length=6).cardinality()
126
sage: IntegerVectors(10, length=6, min_part=1).cardinality()
126
I do not know the exact reasons/history of implementation of
combinatorial objects in Sage. Some of those are now using
IntegerListsLex for enumeration with naive counting, as you noticed.
Regards,
TB
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