Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudoknot RNA structures with arc-length $\ge 4$   In this paper we study $k$-noncrossing RNA structures with minimum arc-length
4 and at most $k-1$ mutually crossing bonds. Let ${\sf T}_{k}^{[4]}(n)$ denote
the number of $k$-noncrossing RNA structures with arc-length $\ge 4$ over $n$
vertices. We prove (a) a functional equation for the generating function
$\sum_{n\ge 0}{\sf T}_{k}^{[4]}(n)z^n$ and (b) derive for $k\le 9$ the
asymptotic formula ${\sf T}_{k}^{[4]}(n)\sim c_k n^{-((k-1)^2+(k-1)/2)}
\gamma_k^{-n}$. Furthermore we explicitly compute the exponential growth rates
$\gamma_k^{-1}$ and asymptotic formulas for $4\le k\le 9$.

11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg