sym-0.9: Permutations, patterns, and statistics

Maintainer Anders Claesson None

Math.Perm.Pattern

Description

Synopsis

# Documentation

type Pattern = PermSource

Pattern is just an alias for permutation.

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`.

subsets :: Int -> Int -> [Set]Source

`subsets n k` is the list of subsets of `[0..n-1]` with `k` elements.

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

`copies p w` is the list of sets that represent copies of `p` in `w`.

`w contains p` is a predicate determining if `w` contains the pattern `p`.

`w avoids p` is a predicate determining if `w` avoids the pattern `p`.

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

`w avoidsAll ps` is a predicate determining if `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`.

minima :: [Pattern] -> [Pattern]Source

The set of minimal elements with respect to containment.

maxima :: [Pattern] -> [Pattern]Source

The set of maximal elements with respect to containment.

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.