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numSemistandardTableaux -- compute the number of semistandard Young tableaux of a given shape

Usage:

numSemistandardTableaux(lam,N)
Inputs:
- lam, an instance of the type Partition, the shape, $\lambda$.
- N, an integer, the maximum entry.
Outputs:
- n, an integer, the number of SSYT of the given shape, and entries in 1..N. If N is not provided, it is assumed to be the length of the shape.

Description

A bagged list of the tableaux can be created with allSemistandardTableaux.

i1 : # allSemistandardTableaux(new Partition from {6,6,5,1,1})

o1 = 2520

i2 : numSemistandardTableaux(new Partition from {6,6,5,1,1})

o2 = 2520

See also

allSemistandardTableaux -- list all semistandard Young tableaux of a given shape

Ways to use numSemistandardTableaux:

numSemistandardTableaux(Partition)
numSemistandardTableaux(Partition,ZZ)

For the programmer

The object numSemistandardTableaux is a method function.

The source of this document is in Tableaux/documentation.m2:1174:0.