By Doron Zeilberger

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Appeared in:
INTEGERS v. 2 (2002), A5.
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.

## SAMPLE Input and Output Files

If you have package UGJ in the same directory as the
input file for UGJ (inUGJ), and type:
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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