The Baxter permutation longest increasing subsequence exponent conjecture

A Baxter permutation of size $n$ is a permutation avoiding the two patterns specified in the source, and bipolar-oriented planar maps with general face degrees correspond to Baxter permutations; under this bijection, the longest increasing subsequence corresponds to the longest directed path. Let $\sigma_n$ be a uniform Baxter permutation of size $n$. Longest increasing subsequence exponent conjecture. The longest increasing subsequence in $\sigma_n$ grows like $n^{3/4}$ as $n\to\infty$. This extends the paper's directed-distance predictions from bipolar-oriented triangulations to bipolar-oriented planar maps with general face-degree distributions, where the conjectured exponent is expected to follow from analogous scaling results.