We derive the algebraic generating function for inversion sequences avoiding the patterns 201 and 210 by describing a set of succession rules, converting them to a system of generating function equations with one catalytic variable, and then solving the system with kernel method techniques.

Permutations are usually enumerated by size, but new results can be found by\nenumerating them by inversions instead, in which case one must restrict one's\nattention to indecomposable permutations. In the style of the seminal paper by\nSimion and Schmidt, we investigate all combinations of permutation patterns of\nlength at most 3.\n

The study of permutation patterns has recently seen several surprising results, and the purpose of this mini-workshop was to bring together researchers from across the field to focus on four hot topics related to these recent developments. The topics covered the nature of generating functions that enumerate permutation classes, the structure of permutation classes and the impact this has on their growth rates, and the study of permutons, which lies at the interface of permutation patterns and discrete probability.…

We prove that any class of permutations defined by avoiding a partially ordered pattern (POP) with height at most two has a regular insertion encoding and thus has a rational generating function. Then, we use Combinatorial Exploration to find combinatorial specifications and generating functions for hundreds of other permutation classes defined by avoiding a size 5 POP, allowing us to resolve several conjectures of Gao and Kitaev (2019) and of Chen and Lin (2024).

We prove that any class of permutations defined by avoiding a partially ordered pattern (POP) with height at most two has a regular insertion encoding and thus has a rational generating function. Then, we use Combinatorial Exploration to find combinatorial specifications and generating functions for hundreds of other permutation classes defined by avoiding a size 5 POP, allowing us to resolve several conjectures of Gao and Kitaev and of Chen and Lin.