论文标题
关于单位间隔订单的编码，Matherne，Morales和Selover的猜想的证明
Proof of a conjecture of Matherne, Morales, and Selover on encodings of unit interval orders
论文作者
论文摘要
从$ n $元素上的单位间隔订单到Dyck路径，有两种近距离订单，从$（0,0）$到$（n，n，n）$。一种是考虑一对无与伦比的元素，这些元素构成了某些戴克路径和对角线之间的一组盒子。另一个是找到一个特定的部分清单（从Guay-Paquet的意义上），该清单产生同构Poset，并将列表列表解释为Dyck路径的区域序列。 Matherne，Morales和Selover猜想，对于任何单位间隔顺序，这两个Dyck路径都与Haglund众所周知的Zeta Belive相关。在本文中，我们证明了他们的猜想。
There are two bijections from unit interval orders on $n$ elements to Dyck paths from $(0,0)$ to $(n,n)$. One is to consider the pairs of incomparable elements, which form the set of boxes between some Dyck path and the diagonal. Another is to find a particular part listing (in the sense of Guay-Paquet) which yields an isomorphic poset, and to interpret the part listing as the area sequence of a Dyck path. Matherne, Morales, and Selover conjectured that, for any unit interval order, these two Dyck paths are related by Haglund's well-known zeta bijection. In this paper we prove their conjecture.
