Posets and spaces of $k$noncrossing RNA Structures
Abstract
RNA molecules are singlestranded 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 PennerWaterman poset, and, using results from the theory of multitriangulations, we show that this is a pure poset of rank $k(2f2k+1)+rf1$, whose geometric realization is the join of a simplicial sphere of dimension $k(f2k)1$ and an $\left((f+1)(k1)1\right)$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.
 Publication:

arXiv eprints
 Pub Date:
 April 2022
 DOI:
 10.48550/arXiv.2204.05934
 arXiv:
 arXiv:2204.05934
 Bibcode:
 2022arXiv220405934M
 Keywords:

 Mathematics  Combinatorics