论文标题
$ k $ -noncrossing RNA结构的POSET和空间
Posets and spaces of $k$-noncrossing RNA Structures
论文作者
论文摘要
RNA分子是DNA的单链类似物，可以折叠成各种结构，这些结构影响其在细胞中的生物学功能。 RNA结构可以用某种称为RNA图的图形进行组合建模。在本文中，我们介绍了一个新的RNA图$ \ MATHCAL {B}^r_ {f，k} $，$ r \ ge 0 $，$ k \ ge 1 $ and $ f \ ge 3 $，我们称之为Penner-waterman poset，以及使用跨度$ k $ k的结果，我们称之为Penner-waterman poset，以及使用$ k $ k的结果。几何实现是尺寸$ k（f-2k）-1 $和$ \ left（（f+1）（k-1）（k-1）-1 \ right）$ - 简单的简单领域的联接，如果$ r = 0 $。作为特殊情况的推论$ k = 1 $，由于彭纳（Penner）和沃特曼（Waterman）关于RNA二级结构的拓扑拓扑，因此获得了结果。这些结果最终可能导致研究RNA $ k $ noncrossing结构的新方法。
RNA molecules are single-stranded analogues of DNA that can fold into various structures which influence their biological function within the cell. RNA structures can be modelled combinatorially in terms of a certain type of graph called an RNA diagram. In this paper we introduce a new poset of RNA diagrams $\mathcal{B}^r_{f,k}$, $r\ge 0$, $k \ge 1$ and $f \ge 3$, which we call the Penner-Waterman poset, and, using results from the theory of multitriangulations, we show that this is a pure poset of rank $k(2f-2k+1)+r-f-1$, whose geometric realization is the join of a simplicial sphere of dimension $k(f-2k)-1$ and an $\left((f+1)(k-1)-1\right)$-simplex in case $r=0$. As a corollary for the special case $k=1$, we obtain a result due to Penner and Waterman concerning the topology of the space of RNA secondary structures. These results could eventually lead to new ways to investigate landscapes of RNA $k$-noncrossing structures.
