lrTableaux -- enumerate Littlewood-Richardson tableaux

Usage:

lrTableaux(lambda, mu, nu)
Inputs:
- lambda, a list, a partition
- mu, a list, a partition contained in lambda
- nu, a list, a partition with |nu| = |lambda| - |mu|
Outputs:
- a list, the list of LR fillings of the skew shape lambda/mu with content nu

Description

An LR tableau is a semistandard skew tableau (rows weakly increasing, columns strictly increasing) whose reverse reading word is a lattice word. Each filling is returned as a list of rows; row $i$ has length $\lambda_i - \mu_i$ and entries in $\{0, \ldots, \#\nu - 1\}$ (so label 0 corresponds to row 1 of $\nu$, etc.). The number of LR tableaux equals the Littlewood-Richardson coefficient $c^\lambda_{\mu,\nu}$.

i1 : #lrTableaux({3,2,1}, {2,1}, {2,1}) -- = c^{(3,2,1)}_{(2,1),(2,1)} = 2

o1 = 2

i2 : #lrTableaux({2,1}, {1}, {1,1})     -- = 1

o2 = 1

Ways to use lrTableaux:

lrTableaux(List,List,List)

For the programmer

The object lrTableaux is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/PieriMaps/doc.m2:469:0.

lrTableaux -- enumerate Littlewood-Richardson tableaux

Description

See also

Ways to use lrTableaux:

For the programmer