In 2006, Chapoton defined a class of Tamari intervals called ”new intervals” in his enumeration of Tamari intervals, and he found that these new intervals are equi-enumerated with bipartite planar maps. We present here a direct bijection between these two classes of objects using a new object called ”degree tree”. Our bijection also gives an intuitive proof of an unpublished equi-distribution result of some statistics on new intervals given by Chapoton and Fusy.

中文翻译：

---

Chapoton 的新区间和二分平面图之间的双射联系

2006 年，Chapoton 在他对 Tamari 区间的枚举中定义了一类称为“新区间”的 Tamari 区间，他发现这些新区间与二部平面图等值枚举。我们在这里使用称为“度数树”的新对象在这两类对象之间呈现直接双射。我们的双射还直观地证明了 Chapoton 和 Fusy 给出的新区间的一些统计数据的未发表等分布结果。