This is a step-by-step guide as to how to compute the data
  from the paper
  "Equivalence classes for the mu-coefficient of Kazhdan-Lusztig
   polynomials in S_n"

Installing
----------
1) Move to a suitable directory.  Extract the C source code via
   tar xvfz klmu-072210.tgz
   (It will be placed in a subdirectory called klmu.)

2) cd klmu

Running
-------

3) ./generate_data.sh

Notes:

0) The various scripts assume you have gcc installed, that perl is in
   a particular standard place, that you are running the zsh shell and
   that you have matlab installed.  I have made no attempt to have
   this all run automatically on your system.  If you have zsh
   installed, you can just include a step 2.5 above: 2.5) zsh

1) On a 3GHz machine, the above script takes a little over 2 days
   to finish computing the databses (the vast majority of which is 
   for n=10).  Computing the equivalence classes takes about one 
   additional day.  

2) Several parameters in generate_data.sh determine for which values
   data will be computed.  Currently, the database of KL polynomials
   will be computed for S_n from n=4 up to n=10.  Code for computing
   for n=11 is included but commented out as it will take forever if
   not run in parallel on a cluster.  The various equivalence classes
   will be computed for n=9,10,11 and with parameter k=0,1,2.  The
   revelant variables are "ub" and "cub" near the beginning of the file.

3) The generate_data.sh script computes the databases of KL-polynomials
   as well as the various equivalence classes described in the paper.
   One can compute the databases only via
      make klep
      for i in {4..10}
      do
          ./klep fileeps $i
	  echo "Done computing EPs for $i"
      done

      ./klep scratch 10

   The above commands will produce four files for each n from 4 to 10:
    n-mult
    n-ep
    n-epidx
    n-idxpoly

   For n=10, n-ep and n-epidx are quite large (about 1 Gig).
   Once they have been constructed there are several simple commands
     available for extracting data:   

   a) ./klep getakl 4
      0213
      3120
      Will read an individual KL poly from the database.

   b) ./klep verify n
      to spit out information about data files
      ./klep vverify n is much more verbose; only use for small n

      for example, running ./klep verify 9 yields
            STATS -9- total eps:         2896168
	    STATS -9- computed eps:      2896168
	    STATS -9- max consec:             11
	    STATS -9- distinct polys:      24322
	    STATS -9- mu eps:              33550
	    STATS -9- num w with eps:      99632
	    STATS -9- maxcoeff: 460

   c) ./klep listp n
      list KL polys that appear in a given S_n

   d) ./klep evalp 
      find max_{x,w \in S_n} P_{x,w}(1)

4) Computation of the equivalence classes will create various files in
   the class subfolder.  (See paper for general description.)  For
   example, there are 51,060 (11,0)-minimal pairs in S_11.  5,166 of
   these have mu=4:

   ~/code/ccode/class% wc 11-c*-m4-k1-*-bare
     4750   9500 114000 11-c1-m4-k1-md0-bare
       16     32    384 11-c2-m4-k1-md0-bare
      384    768   9216 11-c3-m4-k1-md0-bare
       16     32    384 11-c4-m4-k1-md0-bare
     5166  10332 123984 total

   11-c1-m4-k1-md0-bare is a file containing the 4750 (11,0)-minimal
   pairs in S_11 with mu=4 that are not (11,1)-minimal.  In general,
   equivalence class c1 consists of such pairs in the "sink."  The above
   tells us that there are three (11,1)-minimal classes for mu=4 
   consisting of 16, 384 and 16 pairs, respectively.  The above files
   only contain the actual pairs "x w" on each line.  The corresponding
   files ending in "-kl" contain information about the actual K-L 
   polynomials.  

5) Examination of generate_data.sh and the scripts called by it allow
   one to perform individual steps in the data collection process.