Bipartition helpers

This page contains the documentation for various helper functions for manipulating bipartitions.

This page contains the documentation for the bipartition subpackage, that contains helper functions for the Bipartition class.

bipartition.one(f: Bipartition) → Bipartition

Return the identity bipartition with the same degree as the given bipartition.

The identity bipartition of degree \(n\) has blocks \(\{i, -i\}\) for all \(i\in \{0, \ldots, n - 1\}\). This function returns a new identity bipartition of degree equal to the degree of self.

Parameters:

f (Bipartition) – a bipartition

Returns:

A newly constructed Bipartition.

Return type:

Bipartition

bipartition.underlying_partition(f: Bipartition) → list[list[int]]

Return the underlying partition of a Bipartition object. The underlying partition of a bipartition f is the partition of a subset \(P\) of \(\{-n, \ldots, -1\}\cup \{1, \ldots, n\}\) such that:

• \(\{|y|\mid y\in P\} = \{1, \ldots, n\}\) ;

• a block of the partition consists of negative numbers if and only if the corresponding block of y is a transverse block.

Parameters:

f (Bipartition) – the bipartition

Returns:

The underlying partition of the Bipartition.

Return type:

list[list[int]]

Complexity:

\(O(n)\) where \(n\) is the degree().