Posted: Oct. 20, 2019

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,a-1]}
  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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