Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Posets and spaces of $k$-noncrossing RNA Structures   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.

27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph