David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
 Office: 403 McAllister
Phone: (814) 865-3329
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e-mail:dlittle@psu.edu

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Combinatorial Aspects of the Lascoux-Schützenberger Tree

The Bijection

To perform the bijection manually, we begin by selecting a random permutation and a corresponding reduced word. To do so, select both the value of n using B and the type of permutation using C and then press the Random Permutation Button. Alternatively, you may type in your own permutation in region D and then press the Random Reduced Word Button. Let's assume that we have selected the permutation and reduced word as illustrated in the following line diagram.

Now click (double click in the Applet) on the red cross in position 6. This subtracts one from the corresponding letter of the initial reduced word and produces the next line diagram.







































Now click on the newly created red cross in position 2. You may also click on the red cross in position 6 to go back.







































Finally, click on the newly created red cross in position 1, or click on the red cross in position 2 to go back.







































Notice that this final word is reduced and corresponds to a child of our original permutation. On the Applet, you would now push the Update Button to add this new permutation and reduced word to the appropriate list in regions F and G. This entire process can be performed automatically by pushing the -> Button. Click here to view the Applet.