Random words in free groups, non-crossing matchings and RNA secondary structures

Siddhartha Gadgil () and Manjunath Krishnapur ()
Additional contact information
Siddhartha Gadgil: Indian Institute of Science
Manjunath Krishnapur: Indian Institute of Science

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 1, 146-158

Abstract: Abstract Consider a random word $$X^n=(X_1,\ldots ,X_n)$$ X n = ( X 1 , … , X n ) in an alphabet consisting of 4 letters, with the letters viewed either as A, U, G and C (i.e., nucleotides in an RNA sequence) or $$\alpha $$ α , $$\bar{\alpha }$$ α ¯ , $$\beta $$ β and $$\bar{\beta }$$ β ¯ (i.e., generators of the free group $$\langle \alpha ,\beta \rangle $$ ⟨ α , β ⟩ and their inverses). We show that the expected fraction $$\rho (n)$$ ρ ( n ) of unpaired bases in an optimal RNA secondary structure (with only Watson-Crick bonds and no pseudo-knots) converges to a constant $$\lambda _2$$ λ 2 with $$0

Keywords: RNA secondary structure; Noncrossing matchings; Non-abelian free groups; Conjuacy-invariant norms; 20E05; 20F65; 92B05; 60C05; 60J10 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-022-00240-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:54:y:2023:i:1:d:10.1007_s13226-022-00240-x

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-022-00240-x

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().