Systematic counting of restricted partitions

Mingjia Yang, Doron Zeilberger

Research output: Contribution to journalArticlepeer-review


We use ‘partial difference operator schemes’ and dynamical programming to design algorithms that systematically count sets of integer partitions avoiding any set of patterns (of a certain, natural, kind). We describe two approaches, a ‘negative’ (adapting the Goulden–Jackson algorithm for enumerating words), and a ‘positive’ approach that turns out to be much more efficient. Nevertheless, the negative approach has theoretical interest.

Original languageEnglish (US)
Article numberA62
Pages (from-to)1-10
Number of pages10
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics


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