The ‘syt’ package: Young tableaux

The first version of this package dealt with standard Young tableaux only, but now it contains more stuff related to Young tableaux.

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Standard Young tableaux

• Generation of all SYTx of a given shape

• Count of all SYTx of a given shape

• Uniform sampling of SYTx

• Robinson-Schensted correspondence

• Conversion to and from ballot sequences

• Conversion to and from paths on the Young graph

• Plancherel growth process

> gprocess2syt(list(1, 2, c(2,1), c(2,2), c(2,2,1)))
[[1]]
[1] 1 2

[[2]]
[1] 3 4

[[3]]
[1] 5

Other features

• Generation of all semistandard tableaux, possibly skew, with a given shape and a given maximal entry

• Generation of all semistandard tableaux, possibly skew, with a given shape and a given weight

• Generation of all Gelfand-Tsetlin patterns defined by an integer partition, possibly skew, with a given weight

• Computation of Kostka numbers and skew Kostka numbers