-- | A collection of functions to generate, manipulate, -- visualize and count combinatorial objects like partitions, -- compositions, permutations, braids, Young tableaux, -- lattice paths, various tree structures, etc etc. -- -- -- See also the @combinat-diagrams@ library for generating -- graphical representations of (some of) these structure using -- the @diagrams@ library (). -- -- -- The long-term goals are -- -- (1) generate most of the standard structures; -- -- (2) manipulate these structures; -- -- (3) visualize these structures; -- -- (4) the generation should be efficient; -- -- (5) to be able to enumerate the structures -- with constant memory usage; -- -- (6) to be able to randomly sample from them; -- -- (7) finally, to be a repository of algorithms. -- -- -- The short-term goal is simply to generate -- and manipulate many interesting structures. -- -- -- Naming conventions (subject to change): -- -- * prime suffix: additional constrains, typically more general; -- -- * underscore prefix: use plain lists instead of other types with -- enforced invariants; -- -- * \"random\" prefix: generates random objects -- (typically with uniform distribution); -- -- * \"count\" prefix: counting functions. -- -- -- This module re-exports the most commonly used modules. -- module Math.Combinat ( module Math.Combinat.Numbers , module Math.Combinat.Sign , module Math.Combinat.Sets , module Math.Combinat.Tuples , module Math.Combinat.Compositions , module Math.Combinat.Partitions , module Math.Combinat.Permutations , module Math.Combinat.Tableaux , module Math.Combinat.Trees , module Math.Combinat.LatticePaths , module Math.Combinat.ASCII ) where import Math.Combinat.Numbers import Math.Combinat.Sign import Math.Combinat.Sets import Math.Combinat.Tuples import Math.Combinat.Compositions import Math.Combinat.Partitions import Math.Combinat.Permutations import Math.Combinat.Tableaux import Math.Combinat.Trees import Math.Combinat.LatticePaths import Math.Combinat.ASCII