Written: June, 2022

Abstract:

Maple packages

• RedDec.txt, a Maple package for experimenting with reduced decompositions in the symmetrix group, and in particular investigating the number of Yang-Baxter moves

  It also requires the data file YBMdata.txt, to be in the same directory.

• VicR.txt, another Maple package for experimenting with reduced decompositions in the symmetrix group, uses dynamical programming, and hence can go further.

• BalT.txt, A Maple package for experimenting with Balanced tableaux introduced by Paul Edeleman and Curtis Greene:

Sample Input and Output for RedDec.txt

• If you want to see all the Young tableaux of staircase shapes [n-1,...,1] that map to reduced words with Yang-Baxter moves [j+1,j,j+1] or [j,j+1,j] at location i for j=1,..,n-2 and i=1.. n(n-1)-2 for n=4, n=5
  The input file generates the output file  

• If you want to see all the Young tableaux of staircase shapes [n-1,...,1] that map to reduced words with Yang-Baxter moves [j+1.j,j+1] or [j,j+1,j] at location i for j=1,..,n-2 and i=1.. n(n-1)-2 for n=4, n=5, n=6 (Warning: file is big)
  The input file generates the output file  

Sample Input and Output for RedDec.txt

• If you want to see the generating functions according to the statistic "number of Yang-Baxter moves" of the reduced decompositions of the longest permutation [n,n-1,...,1] in the symmetric group S_n for n from 1 to 9 then
  The input file generates the output file  

  Note: this took about 640 seconds.

• If you want to see the generating functions according to the statistic "number of Yang-Baxter moves" of the reduced decompositions of the longest permutation [n,n-1,...,1] in the symmetric group S_n for n from 1 to 10 then
  The input file generates the output file  

  Note: this took much longer: about 20500 seconds.

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