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 language||English (US)|
|Number of pages||10|
|State||Published - 2020|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics