Cat::GradedCombinatorialClass – the category of graded combinatorial classes
Cat::GradedCombinatorialClass represents the category of graded combinatorial classes.
Categories
Details:
A Cat::GradedCombinatorialClass is a Cat::CombinatorialClass equipped with a grading. That is, each object in the combinatorial class has a size which is typically, but not necessarily, a non negative integer.
Such a class is typically infinite; calling the list method without arguments may yield unpredictable results. On the other hand, the existing methods like list, count, generator, or unrank will accept a size as first argument.
Entries
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"typeSize" |
A type for the size; by default Type::NonNegInt. |
size – size of an object (optional).
Cat::GradedCombinatorialClass::size(object x)
Returns the size of an object of the class.
Integer partitions form a graded combinatorial class:
combinat::partitions::hasProp(Cat::GradedCombinatorialClass)
the size of a partition being defined as the sum of its entries:
combinat::partitions::size([4, 3, 2])
We can thus ask for the number of partitions of size 9:
combinat::partitions::count(9)
Changes in MuPAD 3.1
New Function.