Enumeration of Permutation Classes and Weighted Labelled Independent Sets

Publisher's version (útgefin grein)In this paper, we study the staircase encoding of permutations, which maps a permutation to a staircase grid with cellsfilled with permutations. We consider many cases, where restricted to a permutation class, the staircase encoding be-comes a bijection to its image. We describe the image of thoserestrictions using independent sets of graphs weightedwith permutations. We derive the generating function for the independent sets and then for their weighted coun-terparts. The bijections we establish provide the enumeration of permutation classes. We use our results to uncoversome unbalanced Wilf-equivalences of permutation classesand outline how to do random sampling in the permutationclasses. In particular, we cover the classes Av (2314,3124), Av (2413,3142), Av(2413,3124), Av(2413,2134) and Av (2314,2143), as well as many subclasses.Peer reviewe

Enumeration of Permutation Classes and Weighted Labelled Independent Sets

In this paper, we study the staircase encoding of permutations, which maps a permutation to a staircase grid with cells filled with permutations. We consider many cases, where restricted to a permutation class, the staircase encoding becomes a bijection to its image. We describe the image of those restrictions using independent sets of graphs weighted with permutations. We derive the generating function for the independent sets and then for their weighted counterparts. The bijections we establish provide the enumeration of permutation classes. We use our results to uncover some unbalanced Wilf-equivalences of permutation classes and outline how to do random sampling in the permutation classes. In particular, we cover the classes $\mathrm{Av}(2314,3124)$, $\mathrm{Av}(2413,3142)$, $\mathrm{Av}(2413,3124)$, $\mathrm{Av}(2413,2134)$ and $\mathrm{Av}(2314,2143)$, as well as many subclasses.Comment: Final formatting for publication in DMTC

Wilf classification of triples of 4-letter patterns II

this is the second part of a complete paper in arXiv, see 1605.0496