Plotting Ferrer graph of a plane partition

Posted on 2009-07-02 01:23 By NoJ (3)

Categories:

How do I ...? with Maple

I'm currently trying to plot the Ferrers graph of a plane partition, i.e. a 3D structure of stacked boxes.

My input would be a plane partition p_ij with the information ( i, j, k ) for each 'stack of boxes' where i, j are the coordinates in the matrix and k is the value of the respective entry.

As an example, the following input

3 2 1 1
2 2 1
1 1

should produce a plot that looks like this:

Thanks a lot in advance!

Cheers
Nils

One approach using polyhedraplot

Comment on 2009-07-02 08:40 from gulliet ( Maple Rating 3

294)

Let assume that the entries are a list of lists that denotes the height z, i.e. [[3, 2, 1, 1], [2, 2, 1], [1, 1]]. Then, we transform it (manually in the example below) in a list of x-, y-, z-coordinates (for a given point, the x-coordinate is equal to its row index, and, similarly, the y-coordinate is equal to its column index). Finally, we plot the diagram thanks to the function polyhedraplot.

> with(plots); > polyhedraplot([[1, 1, 3], [1, 2, 2], [1, 3, 1], [1, 4, 1], [2, 1, 2], [2, 2, 2], [2, 3, 1], [3, 1, 1], [3, 2, 1]], polyscale = .5, polytype = hexahedron, scaling = CONSTRAINED, orientation = [20, 70]);

HTH,
-- Jean-Marc

Use plots[matrixplot]

Comment on 2009-07-02 11:38 from pchin ( Maple Rating 3

200)

The plots[matrixplot] command, with the heights=histogram option, should provide the functionality you need. There are various examples on the help page to show you how the options work.

Paulina Chin
Maplesoft

Thank you so much Jean-Marc

Comment on 2009-07-02 12:10 from NoJ (3)

Thank you so much Jean-Marc and Paulina, both solutions work like a charm (: