242 research outputs found
Applications in Enumerative Combinatorics of Infinite Weighted Automata and Graphs
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 -Fibonacci Paths using Infinite Weighted Automata
In this paper, we introduce a new family of generalized colored Motzkin
paths, where horizontal steps are colored by means of colors, where
is the th -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
Graph theory and its applications - bibliography, supplement
Coinductive counting with weighted automata
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
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
- …