Drawing Permutations with Few Corners

通过双重偏序集高效计数排列模式

Efficient counting of permutation patterns via double posets

本文将 corner trees 刻画为 twin-tree double posets，并把 Even-Zohar/Leng 算法推广到一类 tree double posets，使更多排列模式可在 O(n^{5/3}) 时间内计数。

通用矩形划分

Generic rectangulations

本文研究了通用矩形划分的计数问题，通过建立与避免特定模式的排列集之间的双射关系，提出了新的计数方法。

On polygon numbers of circle graphs and distance hereditary graphs

Circle graphs are intersection graphs of chords in a circle and $k$-polygon graphs are intersection graphs of chords in a convex $k$-sided polygon where each chord has its endpoints on distinct sides. The $k$-polygon graphs, for $k \ge 2$, form an infinite chain of graph classes, each of which contains the class of permutation graphs. The union of all of those graph classes is the class of circle graphs. The polygon number $\gp(G)$ of a circle graph $G$ is the minimum $k$ such that $G$ is a $k$-polygon graph. Given a circle graph $G$ and an integer $k$, determining whether $\gp(G) \le k$ is NP…