6 papers
The feasible region for consecutive patterns of permutations is a cycle polytope
Jacopo Borga, Raul Penaguiao
We study proportions of consecutive occurrences of permutations of a given size. Specifically, the feasible limits of such proportions on large permutations form a region, called f…
Scaling and local limits of Baxter permutations through coalescent-walk processes
Jacopo Borga, Mickaël Maazoun
Baxter permutations, plane bipolar orientations, and a specific family of walks in the non-negative quadrant are well-known to be related to each other through several bijections.…
The feasible region for consecutive patterns of permutations is a cycle polytope
Jacopo Borga, Raul Penaguiao
We study proportions of consecutive occurrences of permutations of a given size. Specifically, the limit of such proportions on large permutations forms a region, called \emph{feas…
A decorated tree approach to random permutations in substitution-closed classes
Jacopo Borga, Mathilde Bouvel, Valentin Féray +1
We establish a novel bijective encoding that represents permutations as forests of decorated (or enriched) trees. This allows us to prove local convergence of uniform random permut…
Square permutations are typically rectangular
Jacopo Borga, Erik Slivken
We describe the limit (for two topologies) of large uniform random square permutations, i.e., permutations where every point is a record. The starting point for all our results is…
Local convergence for permutations and local limits for uniform -avoiding permutations with
Jacopo Borga
We set up a new notion of local convergence for permutations and we prove a characterization in terms of proportions of \emph{consecutive} pattern occurrences. We also characterize…