Written: May 21, 2001.
This fourth (and last!) sequel to the Foundations article in this Umbral Transfer Matrix series , illustrates how to automatically derive Umbral Schemes for computing generating functions that enumerate words that avoid infintely many "mistakes", or "dirty words".
IMPORTANT: This article is accompanied by three Maple packages
UGJ, that implements the Umbral Goulden-Jackson method
SymUGJ, that does the Symmetric Umbral Goulden-Jackson, and
SiPerUGJ, for the automatic generation of Umbral Schemes for computing generating functions that enumerate families of mistakes that are invariant under the group of Signed Permutations.
Of Related interest is my Maple Analog LinDiophantus of Axel Riese's OMEGA (based on work joint with George Andrews and Peter Paule about MacMahon's Partition Analysis). It might be accompanied by an article one day.
maple -q < inUGJ > oUGJ
then, after a few seconds you should get the output file for UGJ (oUGJ).
If you have package SymUGJ in the same directory as the input file for SymUGJ (inSymUGJ) , and type:
maple -q < inSymUGJ > oSymUGJ
then, after a few minutes you should get the output file for SymUGJ (oSymUGJ).
If you have package SiPerUGJ in the same directory as the first input file for SiPerUGJ(inSiPerUGJ1), and type:
maple -q < inSiPerUGJ1 > oSiPerUGJ1
then, after a few minutes you should get the first output file for SiPerUGJ (oSiPerUGJ1),
If you have package SiPerUGJ in the same directory as the second input file for SiPerUGJ (inSiPerUGJ2), and type:
maple -q < inSiPerUGJ2 > oSiPerUGJ2
then, you should get the second output file for SiPerUGJ (oSiPerUGJ2).
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