Statistical Analysis of Hairpins and BasePairs in RNA Secondary Structures
By AJ Bu, Manuel Kauers, and Doron Zeilberger
.pdf
.tex
Written: Feb. 20, 2026
In memory of Kequan Ding (Changchun, Jilin, China, April 18, 1955 - San Jose, CA, Oct. 21, 2025)
We show the power of symbolic computation by doing precise statistical analysis of
the parameters `hairpins' and `basepairs' in RNA secondary structures.
Mathematica package
AlgAsympt.m,
A Mathematica package to find the asymptotics of sequences of coefficients of algebraic formal power series
Maple packages
-
RNA.txt,
Producing generating functions for the weighted counting of RNA secondary structures.
-
RNAstat.txt,
Statistical analysis of RNA secondary structures.
-
Also needed for deriving the grand-generating function, GGF(X,x,z), hard-coded in RNAstat.txt, is the Maple package
SCHUTZENBERGER.txt,
Sample Input and Output for RNA.txt
-
If you want to see a derivation (and proof!) that the generating function that is the basis of this paper's asymptotic analysis, namely GGF(X,x,z) is correct
the input gives the
output .
Sample Input and Output for RNAstat.txt
If you want to see an article about the asymptotic statistics of Hairpins and Basepairs in RNA secondary structures
the input gives the
output
AJ Bu's Home Page
Manuel Kauers' Home Page
Doron Zeilberger's Home Page