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Members functions

syt.all_sytx(nu)

All standard Young tableaux of given shape.

Parameters:

nu (list of decreasing positive integers) – Integer partition, the shape.

Returns:

The list of all standard Young tableaux of shape nu.

Return type:

list

Examples

>>> from pysyt.syt import all_sytx
>>> all_sytx([3, 2])

syt.count_sytx(nu)

Count all standard Young tableaux of given shape.

Parameters:

nu (list of decreasing positive integers) – Integer partition, the shape.

Returns:

The number of all standard Young tableaux of shape nu.

Return type:

integer

Examples

>>> from pysyt.syt import count_sytx
>>> count_sytx([3, 2])

syt.dual_syt(T)

Dual standard Young tableau.

Parameters:

T (list) – A standard Young tableau.

Returns:

The dual standard Young tableau of T.

Return type:

list

Examples

>>> from pysyt.syt import dual_syt
>>> dual_syt([[1, 3, 5], [2, 4]])

syt.hook_lengths(nu)

Hook lengths of an integer partition.

Parameters:

nu (list of decreasing positive integers) – An integer partition.

Returns:

The hook lengths of nu.

Return type:

list

Examples

>>> from pysyt.syt import hook_lengths
>>> hook_lengths([3, 2])

syt.hooks(nu)

Hooks of an integer partition.

Parameters:

nu (list of decreasing positive integers) – An integer partition.

Returns:

The hooks of nu.

Return type:

list

Examples

>>> from pysyt.syt import hooks
>>> hooks([3, 2])

syt.random_young_path(n)

Young path at random according to the Plancherel growth process.

Parameters:

n (integer) – Size of the path.

Returns:

A path of the Young graph, starting from [1].

Return type:

list

Examples

>>> from pysyt.syt import random_young_path
>>> random_young_path(6)

syt.syt_to_young_path(syt)

Young path corresponding to a standard Young tableau.

Parameters:

syt (list) – A standard Young tableau.

Returns:

A path of the Young graph, starting from [1].

Return type:

list

Examples

>>> from pysyt.syt import syt_to_young_path
>>> syt_to_young_path([[1,2,4], [3], [5]])

syt.young_path_to_syt(path)

Standard Young tableau corresponding to a path on the Young graph.

Parameters:

path (list of integer partitions) – A path on the Young graph, starting from [1].

Returns:

A standard Young tableau.

Return type:

list

Examples

>>> from pysyt.syt import young_path_to_syt
>>> young_path_to_syt([[1], [2], [2,1], [3,1], [3,1,1]])