scholarly journals Delannoy Numbers and Preferential Arrangements

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 238
Author(s):  
Kwang-Wu Chen
Keyword(s):  
Lattice Paths ◽  
Symmetric Identity ◽  
Delannoy Numbers ◽  
Combinatorial Methods

A preferential arrangement on [ [ n ] ] = { 1 , 2 , … , n } is a ranking of the elements of [ [ n ] ] where ties are allowed. The number of preferential arrangements on [ [ n ] ] is denoted by r n . The Delannoy number D ( m , n ) is the number of lattice paths from ( 0 , 0 ) to ( m , n ) in which only east ( 1 , 0 ) , north ( 0 , 1 ) , and northeast ( 1 , 1 ) steps are allowed. We establish a symmetric identity among the numbers r n and D ( p , q ) by means of algebraic and combinatorial methods.

ASYMPTOTICS OF THE WEIGHTED DELANNOY NUMBERS

2012 ◽  
Vol 08 (01) ◽  
pp. 175-188 ◽  
Author(s):  
ROB NOBLE
Keyword(s):  
Number Field ◽  
Asymptotic Expansions ◽  
Lattice Paths ◽  
Delannoy Numbers ◽  
Divisibility Properties ◽  
Special Case

The weighted Delannoy numbers give a weighted count of lattice paths starting at the origin and using only minimal east, north and northeast steps. Full asymptotic expansions exist for various diagonals of the weighted Delannoy numbers. In the particular case of the central weighted Delannoy numbers, certain weights give rise to asymptotic coefficients that lie in a number field. In this paper we apply a generalization of a method of Stoll and Haible to obtain divisibility properties for the asymptotic coefficients in this case. We also provide a similar result for a special case of the diagonal with slope 2.

scholarly journals Combinatorics on lattice paths in strips

2021 ◽  
Vol 94 ◽  
pp. 103310
Author(s):  
Nancy S.S. Gu ◽  
Helmut Prodinger
Keyword(s):  
Lattice Paths

A New Generalization of Delannoy Numbers

2020 ◽  
Vol 51 (4) ◽  
pp. 1729-1735
Author(s):  
Muhammet Cihat Dağli
Keyword(s):  
Delannoy Numbers

Aspects of Job Scheduling

1979 ◽  
Vol 101 (1) ◽  
pp. 17-22 ◽  
Author(s):  
K. Phillips
Keyword(s):  
Job Scheduling ◽  
Scheduling Problem ◽  
Deep Space Network ◽  
Fundamental Parameters ◽  
Space Network ◽  
Plant Operations ◽  
Mathematical Algorithms ◽  
Partitioning Problems ◽  
Combinatorial Methods ◽  
Operational Aspects

A mathematical model for job scheduling in a specified context is presented. The model uses both linear programming and combinatorial methods. While designed with a view toward optimization of scheduling of facility and plant operations at the Deep Space Network (DSN) Station at Goldstone, the context is sufficiently general to be widely applicable. The general scheduling problem including options for scheduling objectives is discussed and fundamental parameters identified. Mathematical algorithms for partitioning problems germaine to scheduling are presented. A more detailed description of algorithms and of operational aspects of the model is planned for a later report.

Transient analysis of M/M/1 queues in discrete time by general server vacations

1994 ◽  
Vol 31 (A) ◽  
pp. 115-129 ◽  
Author(s):  
W. Böhm ◽  
S. G. Mohanty
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Transient Analysis ◽  
Queueing System ◽  
Queueing Model ◽  
Discrete Parameter ◽  
Server Vacations ◽  
Special Case ◽  
Combinatorial Methods ◽  
Transient And Steady State

In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.

scholarly journals Some Identities Involving the Fubini Polynomials and Euler Polynomials

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 300 ◽  
Author(s):  
Guohui Chen ◽  
Li Chen
Keyword(s):  
Power Series ◽  
Second Order ◽  
Euler Polynomials ◽  
Euler Numbers ◽  
Non Linear ◽  
Combinatorial Methods

In this paper, we first introduce a new second-order non-linear recursive polynomials U h , i ( x ) , and then use these recursive polynomials, the properties of the power series and the combinatorial methods to prove some identities involving the Fubini polynomials, Euler polynomials and Euler numbers.

scholarly journals Testing embedded systems using test cases generated through combinatorial techniques

2018 ◽  
Vol 7 (2.7) ◽  
pp. 146
Author(s):  
Lakshmi Prasad Mudarakola ◽  
J K.R. Sastry ◽  
V Chandra Prakash
Keyword(s):  
Embedded Systems ◽  
Embedded System ◽  
Traffic Control ◽  
Nuclear Reactor ◽  
Test Cases ◽  
Critical Systems ◽  
Daily Lives ◽  
Intelligent Devices ◽  
Wireless Infrastructure ◽  
Combinatorial Methods

Thorough testing of embedded systems is required especially when the systems are related to monitoring and controlling the mission critical and safety critical systems. The embedded systems must be tested comprehensively which include testing hardware, software and both together. Embedded systems are highly intelligent devices that are infiltrating our daily lives such as the mobile in your pocket, and wireless infrastructure behind it, routers, home theatre system, the air traffic control station etc. Software now makes up 90% of the value of these devices. In this paper, authors present different methods to test an embedded system using test cases generated through combinatorial techniques. The experimental results for testing a TMCNRS (Temperature Monitoring and Controlling Nuclear Reactor System) using test cases generated from combinatorial methods are also shown.

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