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ENUMERATION OF CHORD DIAGRAMS ON MANY INTERVALS AND THEIR NONORIENTABLE ANALOGS
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On topological RNA interaction structures
, 2012
"... Recently a folding algorithm of topological RNA pseudoknot structures has been presented [24]. This algorithm folds single stranded γstructures, i.e. RNA structures composed by distinct motifs of bounded topological genus. In this paper, we study the two backbone analogue of γstructures: the RNA γ ..."
Abstract

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Recently a folding algorithm of topological RNA pseudoknot structures has been presented [24]. This algorithm folds single stranded γstructures, i.e. RNA structures composed by distinct motifs of bounded topological genus. In this paper, we study the two backbone analogue of γstructures: the RNA γinteraction structures. These are RNARNA interaction structures that are constructed by a finite number of building blocks over two and one backbone having genus at most γ. Properties of γinteraction structures are of practical interest since they are the targets of topological interaction structure folding algorithms. We show that the generating function of γinteraction structures is algebraic, which implies that the numbers of interaction structures can be computed recursively. We furthermore obtain simple asymptotic formulas for 0 and 1interaction structures. The simplest class are the 0interaction structures, which represent the two backbone analogue of secondary structures.
Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces
 NUCL. PHYS. B
, 2012
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