Modular, $k$-Noncrossing Diagrams
نویسندگان
چکیده
منابع مشابه
Modular, k-Noncrossing Diagrams
In this paper we compute the generating function of modular, k-noncrossing diagrams. A k-noncrossing diagram is called modular if it does not contain any isolated arcs and any arc has length at least four. Modular diagrams represent the deformation retracts of RNA tertiary structures and their properties reflect basic features of these bio-molecules. The particular case of modular noncrossing d...
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In this paper we enumerate k-noncrossing tangled-diagrams. A tangled-diagram is a labeled graph whose vertices are 1, . . . , n have degree ≤ 2, and are arranged in increasing order in a horizontal line. Its arcs are drawn in the upper halfplane with a particular notion of crossings and nestings. Our main result is the asymptotic formula for the number of knoncrossing tangled-diagrams Tk(n) ∼ c...
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We give a correspondence between graphs with a given degree sequence and fillings of Ferrers diagrams by nonnegative integers with prescribed row and column sums. In this setting, k-crossings and k-nestings of the graph become occurrences of the identity and the antiidentity matrices in the filling. We use this to show the equality of the numbers of k-noncrossing and k-nonnesting graphs with a ...
متن کاملON k-NONCROSSING PARTITIONS
In this paper we prove a duality between k-noncrossing partitions over [n] = {1, . . . , n} and k-noncrossing braids over [n − 1]. This duality is derived directly via (generalized) vacillating tableaux which are in correspondence to tangled-diagrams [6]. We give a combinatorial interpretation of the bijection in terms of the contraction of arcs of tangled-diagrams. Furthermore it induces by re...
متن کاملHopf Algebras on Decorated Noncrossing Arc Diagrams
Noncrossing arc diagrams are combinatorial models for the equivalence classes of the lattice congruences of the weak order on permutations. In this paper, we provide a general method to endow these objects with Hopf algebra structures. Specific instances of this method produce relevant Hopf algebras that appeared earlier in the literature.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2010
ISSN: 1077-8926
DOI: 10.37236/348