Combinatorics Namespace Reference

Classes
struct	Error
class	Factorial
	Functor for computation of the factorial function; with helper function factorial. More...
class	Descending_power
	Functor for computation of descending powers; with helper function descending_power. More...
class	Binom_integer_over_integer
	Functor for computing integral binomial coefficients; with helper function binom_integer_over_integer. More...
Enumerations
enum	choose_possibilities { no_subsets = -1, no_further_subsets = 0, further_subsets = 1 }
	Function for running through all k-subsets of an n-set in lexicographical order. More...
Functions
template<typename Int >
Int	factorial (const Int &n)
template<typename Num , typename Int >
Num	descending_power (Num b, Int k)
template<typename Int >
Int	binom_integer_over_integer (const Int z, const Int k)
template<typename Int >
Int	binom (Int a, Int b)
template<typename Int , class ForwardIterator >
choose_possibilities	choose_next (const Int n, const Int k, const ForwardIterator begin, const ForwardIterator end)

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Enumeration Type Documentation

enum Combinatorics::choose_possibilities

Function for running through all k-subsets of an n-set in lexicographical order.

Given a subset as the range of elements, sorted in ascending order, modify the range to the next subset in lexicographical order, if possible.

See ComputerAlgebra/Combinatorics/Lisp/Enumeration/Subsets.mac for the procedural specification at Maxima/Lisp level.

Todo:

See "Iteration through lexicographical order" in ComputerAlgebra/Combinatorics/Lisp/Enumeration/plans/Subsets.hpp.

Todo:

The implementation is not very efficient; improve it.

Todo:

The design should be perhaps be iterator-based.

Enumerator:

no_subsets
no_further_subsets
further_subsets

Definition at line 168 of file Combinatorics.hpp.

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Function Documentation

template<typename Int >

Int Combinatorics::binom	(	Int	a,
		Int	b
	)		[inline]

Definition at line 139 of file Combinatorics.hpp.

template<typename Int >

Int Combinatorics::binom_integer_over_integer	(	const Int	z,
		const Int	k
	)		[inline]

Definition at line 135 of file Combinatorics.hpp.

template<typename Int , class ForwardIterator >

choose_possibilities Combinatorics::choose_next	(	const Int	n,
		const Int	k,
		const ForwardIterator	begin,
		const ForwardIterator	end
	)

Definition at line 170 of file Combinatorics.hpp.

References Latex_Handler::begin(), further_subsets, no_further_subsets, and no_subsets.

Referenced by Ramsey::Enumerate_hyperedges< Int >::next().

template<typename Num , typename Int >

Num Combinatorics::descending_power	(	Num	b,
		Int	k
	)		[inline]

Definition at line 81 of file Combinatorics.hpp.

template<typename Int >

Int Combinatorics::factorial

(

const Int &

n

)

[inline]

Definition at line 60 of file Combinatorics.hpp.

Referenced by OKlib::HypergraphColouring::Greedy_colouring< UndirectedGraph >::evaluation().