242 research outputs found

    Applications in Enumerative Combinatorics of Infinite Weighted Automata and Graphs

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    In this paper, we present a general methodology to solve a wide variety of classical lattice path counting problems in a uniform way. These counting problems are related to Dyck paths, Motzkin paths and some generalizations. The methodology uses weighted automata, equations of ordinary generating functions and continued fractions. This new methodology is called Counting Automata Methodology. It is a variation of the technique proposed by Rutten, which is called Coinductive Counting

    Enumeration of kk-Fibonacci Paths using Infinite Weighted Automata

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    In this paper, we introduce a new family of generalized colored Motzkin paths, where horizontal steps are colored by means of Fk,lF_{k,l} colors, where Fk,lF_{k,l} is the llth kk-Fibonacci number. We study the enumeration of this family according to the length. For this, we use infinite weighted automata.Comment: arXiv admin note: substantial text overlap with arXiv:1310.244

    An extensive English language bibliography on graph theory and its applications, supplement 1

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    Graph theory and its applications - bibliography, supplement

    Coinductive counting with weighted automata

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    A general methodology is developed to compute the solution of a wide variety of basic counting problems in a uniform way: (1) the objects to be counted are enumerated by means of an infinite weighted automaton; (2) the automaton is reduced by means of the quantitative notion of stream bisimulation; (3) the reduced automaton is used to compute

    Use of Enumerative Combinatorics for proving the applicability of an asymptotic stability result on discrete-time SIS epidemics in complex networks

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    In this paper, we justify by the use of Enumerative Combinatorics, that the results obtained in \cite{Alarcon1}, where is analysed the complex dynamics of an epidemic model to identify the nodes that contribute the most to the propagation process and because of that are good candidates to be controlled in the network in order to stabilize the network to reach the extinction state, is applicable in almost all the cases. The model analysed was proposed in \cite{Gomez1} %et al. [Phys.Rev.E 84, 036105(2011)] and results obtained in \cite{Alarcon1} implies that it is not necessary to control all nodes, but only a minimal set of nodes if the topology of the network is not regular. This result could be important in the spirit of considering policies of isolation or quarantine of those nodes to be controlled. Simulation results were presented in \cite{Alarcon1} for large free-scale and regular networks, that corroborate the theoretical findings. In this article we justify the applicability of the controllability result obtained in \cite{Alarcon1} in almost all the cases by means of the use of Combinatorics. {\em Mathematics Subjects Classification}: 05A16,34H20,58E25 {\em Keywords}: Asymptotic Graph Enumeration Problems; Network control; virus spreading

    Bibliographie

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