libsemigroups::blocks Namespace Reference

This namespace contains helper functions for the Blocks class.

Functions
void	throw_if_invalid (Blocks const &x)
	Check a Blocks object.
std::vector< std::vector< int32_t > >	underlying_partition (Blocks const &x)
	Return the underlying partition of a Blocks object.

Function Documentation

throw_if_invalid()

void throw_if_invalid

(

Blocks const &

x

)

This function checks a Blocks object, and throws an exception if the object does not:

• consist of non-negative integers; and
• have the property that if \(i\), \(i > 0\) occurs in x, then \(i - 1\) occurs earlier in x.

The value of x[i] should represent the index of the block containing i.

For example, if x is {0, 1, 1, 2, 1, 1, 3, 1, 1, 4, 5, 6}, then the above conditions are satisfied, but if x is {1, 0, 1, 10} then they are not.

Parameters

x	the blocks object to check.

Exceptions

LibsemigroupsException

if x is invalid.

underlying_partition()

std::vector< std::vector< int32_t > > underlying_partition ( Blocks const & x )

nodiscard

The underlying partition of a Blocks object x is the partition of a subset \(P\) of \(\{-n, \ldots, -1\}\cup \{1, \ldots, n\}\) such that:

• \(\{|x|\mid x\in P\} = \{1, \ldots, n\}\);
• a block of the partition consists of negative numbers if and only if the corresponding block of x is a transverse block.

Parameters

x	the Blocks object.

Returns

A vector of vectors of integers.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

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