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syt (version 0.5.0)

Young Tableaux

Description

Deals with Young tableaux (field of combinatorics). For standard Young tabeaux, performs enumeration, counting, random generation, the Robinson-Schensted correspondence, and conversion to and from paths on the Young lattice. Also performs enumeration and counting of semistandard Young tableaux, enumeration of skew semistandard Young tableaux, enumeration of Gelfand-Tsetlin patterns, and computation of Kostka numbers.

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Install

install.packages('syt')

Monthly Downloads

243

Version

0.5.0

License

GPL-3

Issues

0

Pull Requests

0

Stars

3

Forks

0

Maintainer

Stc3<a9>phane Laurent

Last Published

July 23rd, 2024

Functions in syt (0.5.0)

count_sytx

Number of standard Young tableaux
prettyTableau

Pretty tableau
gprocess2syt

Growth process to tableau
syt2matrix

Standard Young tableau as sparse matrix
syt2gprocess

Tableau as growth process
isSkewTableau

Check whether a tableau is a skew tableau
hooklengths

Hook lengths
rsyt

Random standard Young tableau
skewGelfandTsetlinPatterns

Skew Gelfand-Tsetlin patterns
tableau2matrix

Tableau as sparse matrix
nextsyt

Next tableau
tableauShape

Shape of a tableau
isStandardSkewTableau

Check whether a skew tableau is standard
matrix2syt

Standard Young tableau from a matrix
rgprocess

Plancherel growth process
syt2ballot

Tableau as ballot sequence
ssytx_withGivenShapeAndWeight

Semistandard Young tableaux with given shape and weight
dualSkewTableau

Dual skew tableau
dualTableau

Dual tableau
isSYT

Checks whether a tableau is standard
isSemistandardSkewTableau

Check whether a skew tableau is semistandard
skewTableauxWithGivenShapeAndWeight

Skew semistandard tableaux with given shape and weight
skewKostkaNumbers

Skew Kostka numbers
prettyGT

Pretty Gelfand-Tsetlin pattern
prettySkewTableau

Pretty skew tableau
KostkaNumbers

Kostka numbers for all partitions of a given weight
KostkaNumbersWithGivenLambda

Kostka numbers with given \(\lambda\)
all_ssytx

Enumeration of semistandard Young tableaux
KostkaNumbersWithGivenMu

Kostka numbers with given \(\mu\)
all_sytx

Enumeration of standard Young tableaux
KostkaNumber

Kostka number
GelfandTsetlinPatterns

Gelfand-Tsetlin patterns
RS

Robinson-Schensted correspondence
ballot2syt

Tableau as ballot sequence
all_ssSkewTableaux

Semistandard skew tableaux
isSSYT

Checks whether a tableau is semistandard
hooks

Hooks
dualsyt

Dual tableau
count_ssytx

Number of semistandard Young tableaux
firstsyt

First tableau of a given shape