Blocks¶

class Blocks¶

Defined bipart.hpp.

Blocks is a class representing signed partitions of the set \(\{0, \ldots, n - 1\}\).

It is possible to associate to every Bipartition a pair of blocks, Bipartition::left_blocks() and Bipartition::right_blocks(), which determine the Green’s \(\mathscr{L}\)- and \(\mathscr{R}\)-classes of the Bipartition in the monoid of all bipartitions. This is the purpose of this class.

The Blocks class is not currently used widely in libsemigroups but are used extensively in the GAP package Semigroups package for GAP.

Member types¶

`const_iterator`	Type for const iterators pointing to the index of the block.
`iterator`	Type for iterators pointing to the index of the block.
`lookup_const_iterator`	Type for const iterators pointing to the transverse block lookup.

`Blocks() noexcept = default`	Constructs a blocks object of size 0.
`Blocks(Blocks const&) = default`	Default copy constructor.
`Blocks(Blocks&&) = default`	Default move constructor.
`Blocks(const_iterator,const_iterator)`	Constructs a blocks object from iterators.
`Blocks(size_t)`	Constructs a blocks object of given degree.
`operator=(Blocks const&) = default`	Default copy assignment operator.
`operator=(Blocks&&) = default`	Default move assignment operator.

`set_block(size_t, uint32_t)`	Set the block that a point belongs to.
`set_is_transverse_block(size_t, bool)`	Set whether or not the block containing a point is transverse.

`operator!=(Blocks const&) const`	Compare two blocks objects for inequality.
`operator<(Blocks const&) const`	Compare two blocks objects for less.
`operator==(Blocks const&) const`	Compare two blocks objects for equality.
`operator[](size_t) const`	Returns a const reference to the index of the block containing a point.

`degree() const noexcept`	Returns the degree of a blocks object.
`hash_value() const noexcept`	Returns a hash value for a `Blocks` instance.
`is_transverse_block(size_t) const noexcept`	Check if a block is a transverse block.
`number_of_blocks() const noexcept`	Returns the number of blocks in a `Blocks` object.
`rank() const`	Returns the number of transverse blocks.

`cbegin() const noexcept`	Returns a const iterator pointing to the index of the first block.
`cbegin_lookup() const noexcept`	Returns a const iterator pointing to the first transverse block lookup.
`cend() const noexcept`	Returns a const iterator pointing one past-the-end of the last block.
`cend_lookup() const noexcept`	Returns a const iterator pointing to the first transverse block lookup.