utils

Set of auxiliary functions used across the project.

utils.get_partitions(n: int) → list[tuple[int]]

Returns a list of all partitions of n.

Parameters:

n (int) – Integer to partition

Returns:

List of all partitions of n.

Return type:

list[tuple[int]]

utils.majorize(mu: tuple[int], ell: tuple[int], eq=True) → bool

Determines if lambda >= Mu in majorization order

Parameters:

• mu (tuple[int]) – Partition as a list of positive integers in nonincreasing order.

• ell (tuple[int]) – Partition as a list of positive integers in nonincreasing order.

• eq – Flag for requiring that Mu and Lambda are partitions of the same number

Returns:

True if Lambda >= Mu in majorization order, False otherwise.

Return type:

bool

utils.partitions(n: int, minimum_partition_value: int = 1)

Returns a generator that yields all partitions of n.

Source: https://stackoverflow.com/questions/10035752/elegant-python-code-for-integer-partitioning

Parameters:

• n (int) – Integer to partition

• minimum_partition_value (int, optional) – Minimum partition value. Defaults to 1.

utils.perm_module_d(mu: tuple[int]) → int

Returns the dimension of the permutation module of label Mu

Parameters:

Mu (tuple[int]) – Partition as a list of positive integers in nonincreasing order that sum up to n.

Returns:

Dimension of the permutation module of label Mu

Return type:

int