Safe Haskell | None |
---|---|
Language | Haskell2010 |
Mobius inversion for the coarsening poset of partitions
Synopsis
- newtype Partition = Partition [Int]
- coarserThan :: Partition -> Partition -> Bool
- finerThan :: Partition -> Partition -> Bool
- (.==.) :: Partition -> Partition -> Bool
- (./=.) :: Partition -> Partition -> Bool
- (.<=.) :: Partition -> Partition -> Bool
- (.>=.) :: Partition -> Partition -> Bool
- (.<.) :: Partition -> Partition -> Bool
- (.>.) :: Partition -> Partition -> Bool
- fastClosure :: Partition -> Set Partition
- fastAntiClosure :: Partition -> Set Partition
- closureSet :: Partition -> Set Partition
- closureSet' :: Partition -> Set Partition
- zetaOf :: Partition -> ZMod Partition
- mobiusOf :: Partition -> ZMod Partition
- firstLevelDown :: Partition -> [Partition]
- firstLevelUp :: Partition -> [Partition]
- closureSetOfSetPartition :: SetPartition -> Set SetPartition
- firstLevelDownSetP :: SetPartition -> [SetPartition]
Documentation
A partition of an integer. The additional invariant enforced here is that partitions
are monotone decreasing sequences of positive integers. The Ord
instance is lexicographical.
Instances
Eq Partition | |
Ord Partition | |
Defined in Math.Combinat.Partitions.Integer.Naive | |
Read Partition | |
Show Partition | |
CanBeEmpty Partition | |
HasNumberOfParts Partition | |
Defined in Math.Combinat.Partitions.Integer.Naive numberOfParts :: Partition -> Int # | |
HasWidth Partition | |
Defined in Math.Combinat.Partitions.Integer.Naive | |
HasHeight Partition | |
Defined in Math.Combinat.Partitions.Integer.Naive | |
HasWeight Partition | |
Defined in Math.Combinat.Partitions.Integer.Naive | |
HasDuality Partition | |
Defined in Math.Combinat.Partitions.Integer.Naive | |
Mathematica Partition Source # | |
Defined in Math.RootLoci.Misc.Common mathematica :: Partition -> String Source # | |
CacheKey Partition Source # | |
The refinement poset of partitions
closures
fastAntiClosure :: Partition -> Set Partition Source #
Fast computation of a single "anticlosure" (opposite poset)
closureSet :: Partition -> Set Partition Source #
Caches and reuses all closures (lazily), this is the fastest version
Mobius function
helpers
firstLevelDown :: Partition -> [Partition] Source #
Merging two parts
firstLevelUp :: Partition -> [Partition] Source #
Splitting one part into two