Systematic Counting of Restricted Partitions
By Mingjia Yang and Doron Zeilberger
.pdf
.tex
[Published in INTEGERS v. 20 (2020), A62]
First Posted: Oct. 20, 2019; Slightly revised version: April 12, 2020.
Integer partitions are one of the most fundamental objects of combinatorics (and number theory), and so is enumerating
objects avoiding patterns. In the present paper we present two approaches for the
systematic counting of classes of partitions avoiding an arbitrary set of "patterns".
Maple packages

RPpos.txt,
a Maple package to enumerate partitions
avoiding any set of "patterns", using the POSITIVE approach

RPneg.txt,
a Maple package to enumerate partitions with specified largest part and number of parts
avoiding any set of "patterns", using the NEGATIVE approach.
Warning: this package is only of theoretical interest and for checking purposes.
It is much slower than the above program.
Sample Input and Output for RPpos.txt

If you want to see the the first, 300, terms of all the enumerating sequences of partitions
avoiding sets of up to , 3, patterns each of length up to , 3, whose entries are from 0 to 1
The input file
yields the output file
Sample Input and Output for RPneg.txt

If you want to see the the first, 25, terms of the enumerating sequence for partitions
avoiding the patterns {[a,a,a], [a,a,a1]}
The input file
yields the output file
As you can see, this is very slow. Just for comparison, using RPpos.txt, we get, much faster.
The input file
yields the output file
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