Maintainer | Anders Claesson <anders.claesson@gmail.com> |
---|---|

Safe Haskell | None |

- type Pattern = Perm
- type Set = CLongArray
- ordiso :: Perm -> Perm -> Set -> Bool
- subsets :: Int -> Int -> [Set]
- copiesOf :: Pattern -> Perm -> [Set]
- contains :: Perm -> Pattern -> Bool
- avoids :: Perm -> Pattern -> Bool
- avoidsAll :: Perm -> [Pattern] -> Bool
- avoiders :: [Pattern] -> [Perm] -> [Perm]
- minima :: [Pattern] -> [Pattern]
- maxima :: [Pattern] -> [Pattern]
- coeff :: (Pattern -> Int) -> Pattern -> Int

# Documentation

type Set = CLongArraySource

A set is represented by an increasing array of non-negative integers.

ordiso :: Perm -> Perm -> Set -> BoolSource

`ordiso u v m`

determines whether the subword in `v`

specified by
`m`

is order isomorphic to `u`

.

copiesOf :: Pattern -> Perm -> [Set]Source

`copies p w`

is the list of sets that represent copies of `p`

in `w`

.

contains :: Perm -> Pattern -> BoolSource

`w `

is a predicate determining if `contains`

p`w`

contains the pattern `p`

.

avoids :: Perm -> Pattern -> BoolSource

`w `

is a predicate determining if `avoids`

p`w`

avoids the pattern `p`

.

avoidsAll :: Perm -> [Pattern] -> BoolSource

`w `

is a predicate determining if `avoidsAll`

ps`w`

avoids the patterns `ps`

.

avoiders :: [Pattern] -> [Perm] -> [Perm]Source

`avoiders ps ws`

is the list of permutations in `ws`

avoiding the
patterns in `ps`

.

coeff :: (Pattern -> Int) -> Pattern -> IntSource

`coeff f v`

is the coefficient of `v`

when expanding the
permutation statistic `f`

as a sum of permutations/patterns. See
Petter Brändén and Anders Claesson: Mesh patterns and the expansion
of permutation statistics as sums of permutation patterns, The
Electronic Journal of Combinatorics 18(2) (2011),
http://www.combinatorics.org/ojs/index.php/eljc/article/view/v18i2p5.