We construct a new family of random permutons, called skew Brownian permuton, which describes the limits of various models of random constrained permutations. This family is parametrized by two real parameters. For a specific choice of the parameters, the skew Brownian permuton coincides with the Baxter permuton, i.e. the permuton limit of Baxter permutations. We …
We recently introduced a new universal family of permutons, depending on two parameters, called skew Brownian permuton. For some specific choices of the parameters, the skew Brownian permuton coincides with some previously studied permutons: the biased Brownian separable permuton and the Baxter permuton. The latter two permutons are degenerate cases of the skew Brownian permuton. In …
We study the feasible region for consecutive patterns of pattern-avoiding permutations. More precisely, given a family of permutations avoiding a fixed set of patterns, we study the limit of proportions of consecutive patterns on large permutations of . These limits form a region, which we call the pattern-avoiding feasible region for . We show that, …