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# gtPatterns -- a list of Gelfand-Tsetlin patterns of shape lambda

- Usage:
    `gtPattern(lambda)`
- Inputs:
  - lambda, a list,
- Outputs:
  - L, a list,

## Description

Currently only supported for $\mathfrak{g} = sl_n$.

This function computes a list of Gelfand-Tsetlin patterns of shape $\lambda$ by computing the lattice points of the Gelfand-Tsetlin polytope. See the documentation for GTPattern and gtPolytope for more details.

    i1 : gtPatterns("A",{2,0,0})

    o1 = {{2, 0, 0, 2, 0, 2}, {2, 0, 0, 2, 0, 1}, {2, 0, 0, 2, 0, 0}, {2, 0, 0,
         ------------------------------------------------------------------------
         1, 0, 1}, {2, 0, 0, 1, 0, 0}, {2, 0, 0, 0, 0, 0}}

    o1 : List

We compare this to the lattice points of the Gelfand-Tsetlin polytope for this shape.

    i2 : P = gtPolytope("A",{2,0,0})

    o2 = P

    o2 : Polyhedron

    i3 : latticePoints(P)

    o3 = {| 2 |, | 2 |, | 2 |, | 2 |, | 2 |, | 2 |}
          | 0 |  | 0 |  | 0 |  | 0 |  | 0 |  | 0 |
          | 0 |  | 0 |  | 0 |  | 0 |  | 0 |  | 0 |
          | 0 |  | 1 |  | 1 |  | 2 |  | 2 |  | 2 |
          | 0 |  | 0 |  | 0 |  | 0 |  | 0 |  | 0 |
          | 0 |  | 0 |  | 1 |  | 0 |  | 1 |  | 2 |

    o3 : List

## Ways to use gtPatterns:

- `gtPatterns(String,List)`

## For the programmer

The object gtPatterns is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/LieAlgebraRepresentations/documentation.m2:2316:0.