Three Hoppy path problems and ternary paths
نویسندگان
چکیده
In this paper we solve several recurrence relations with two (three) indices using combinatorial methods. Moreover, we present several recurrence relations with two (three) indices related to ternary paths and k-ary paths. © 2007 Elsevier B.V. All rights reserved. MSC: 10A35; 65Q05; 05.10
منابع مشابه
ALGORITHMS FOR BIOBJECTIVE SHORTEST PATH PROBLEMS IN FUZZY NETWORKS
We consider biobjective shortest path problems in networks with fuzzy arc lengths. Considering the available studies for single objective shortest path problems in fuzzy networks, using a distance function for comparison of fuzzy numbers, we propose three approaches for solving the biobjective prob- lems. The rst and second approaches are extensions of the labeling method to solve the sing...
متن کاملOn an Optimality Property of Ternary Trees
In the book of Knuth (1972) an extensive discussion can be found on some problems concerning rooted trees. Given a prescribed number of end-vertices, one may ask for the binary (or ternary) tree with minimal external path length (i.e. minimal sum of path lengths from the root to end-vertices), or minimal weighted external path length (here the end-vertices have given weights). In the first case...
متن کاملReturns and Hills on Generalized Dyck Paths
In 2009, Shapiro posed the following question: “What is the asymptotic proportion of Dyck paths having an even number of hills?” In this paper, we answer Shapiro’s question, as well as a generalization of the question to ternary paths. We find that the probability that a randomly chosen ternary path has an even number of hills approaches 125/169 as the length of the path approaches infinity. Ou...
متن کاملAnalysis of Frequency Leakage in Different Optical Paths of Nano-Metrology Systems Based on Frequency-Path Models
The drawing of frequency-path (F-P) models of optical beams is an approach for nonlinearity analysis in nano-metrology systems and sensors based on the laser interferometers. In this paper, the frequency-path models of four nano-metrology laser interferometry systems are designed, analyzed and simulated, including ...
متن کاملEstimation of Fracture path in the Structures and the Influences of Non-singular term on crack propagation
In the present research, a fully Automatic crack propagation as one of the most complicated issues in fracture mechanics is studied whether there is an inclusion or no inclusion in the structures. In this study The Extended Finite Element Method (XFEM) is utilized because of several drawbacks in standard finite element method in crack propagation modeling. Estimated Crack paths are obtained by ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 156 شماره
صفحات -
تاریخ انتشار 2008