Maintainer	Anders Claesson <anders.claesson@gmail.com>
Safe Haskell	None

Sym.Perm.SSYT

Description

Data types for Semistandard Young Tableaux (SSYT) and functions for converting between (generalized) permutataions and SSYT. In other words, this module implements the Robinson-Schensted-Knuth (RSK) correspondence.

Synopsis

Documentation

type GeneralizedPerm = [(Int, Int)]Source

A Generalized Permutation is a lexicographically sorted list of pairs of non-negative integers.

type Entry = Int Source

An entry is a non-negative integer

type SSYT = [[Entry]]Source

A Semistandard Young Tableau (SSYT): the entries weakly increase along each row and strictly increase down each column.

data SSYTPair Source

A pair of Semistandard Young Tableaux.

Constructors

SSYTPair
Fields insertionTableau :: SSYT recordingTableau :: SSYT

Instances

Eq SSYTPair
Show SSYTPair
Shape SSYTPair
Permutation SSYTPair

class Shape a whereSource

Methods

shape :: a -> [Int]Source

Instances

Shape SSYTPair
Shape SSYT

empty :: SSYTPair Source

A pair of empty Young tableaux.

null :: SSYTPair -> Bool Source

Check if a given pair of Young tableaux are empty.

display :: SSYTPair -> String Source

Produce a string for pretty printing SSYT pairs.

fromPerm :: Perm -> SSYTPair Source

The Robinson-Schensted algorithm.

fromGeneralizedPerm :: GeneralizedPerm -> SSYTPair Source

The Robinson-Schensted-Knuth (RSK) algorithm.

toPerm :: SSYTPair -> Perm Source

The inverse of the Robinson-Schensted algorithm.

toGeneralizedPerm :: SSYTPair -> GeneralizedPerm Source

The inverse of the Robinson-Schensted-Knuth algorithm.