numerical_set¶
- class pocketpartition.core.numerical_set.NumericalSet(gaps)[source]¶
Bases:
object- property gaps¶
- property frobenius_number¶
- atom_monoid_gaps()[source]¶
Compute the gaps of the atom monoid.
Returns: set of int: The gaps of the atom monoid.
- partition()[source]¶
Creates a partition based on a specific walk profile using the gaps attribute.
The walk is defined as follows: - Start at 0. - If the current number is in gaps, move up (create a new row with the same length as the current row). - If the current number is not in gaps, move right (add one box to the current row). - Continue this process until reaching the maximum number in gaps. - Collect the lengths of each row at the end of the walk.
The resulting partition is returned as a list of integers in non-increasing order.
Returns: list: A partition [a1, a2, …, an] in non-increasing order, representing the profile of the walk.