跳至主要内容

Generalization of Some Problems with s-Separation

Read  full  paper  at:
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=52954#.VK3lAsnQrzE

ABSTRACT
In this article we apply and discuss El-Desouky technique to derive a generalization of the problem of selecting k balls from an n-line with no two adjacent balls being s-separation. We solve the problem in which the separation of the adjacent elements is not having odd and even separation. Also we enumerate the number of ways of selecting k objects from n-line objects with no two adjacent being of separations m, m + 1, …, pm, where p is positive integer. Moreover we discuss some applications on these problems.
 
Cite this paper
El-Desouky, B. , Gad, M. and El-Eraqy, S. (2015) Generalization of Some Problems with s-Separation. Applied Mathematics, 6, 1-6. doi: 10.4236/am.2015.61001.
 
References
[1]Kplansky, I. (1943) Solution of the “Problems des Ménages”. Bulletin of the American Mathematical Society, 49, 784-785.
http://dx.doi.org/10.1090/S0002-9904-1943-08035-4
 
[2]Riordan, J. (1958) An Introduction to Combinatorial Analysis. Wiley, New York.
 
[3]Moser, W.O.J. (1986) The Number of Subsets without a Fixed Circular Distance. Journal of Combinatorial Theory, Series A, 43, 130-132.
http://dx.doi.org/10.1016/0097-3165(86)90030-0
 
[4]El-Desouky, B.S. (1988) On Selecting k Balls from an n-Line without Unit Separation. Indian Journal of Pure and Applied Mathematics, 19, 145-148.
 
[5]El-Desouky, B.S. (1988) Selecting k Balls without s-Separation. The 23rd Annual Conference on Statistics, Computer Science, Operations Research and Mathematics, Cairo, December 1988, 40-46.
 
[6]Mansour, T. and Sun, Y.D. (2008) On Selecting the Number of Combinations without Certain Separations. European Journal of Combinatorics, 29, 1200-1206.
http://dx.doi.org/10.1016/j.ejc.2007.06.024
 
[7]Mansour, T. (2014) Set Partitions with Circular Successions. European Journal of Combinatorics, 41, 207-216.
http://dx.doi.org/10.1016/j.ejc.2014.06.008
 
[8]Gourden, J.P. and Jackson, D.M. (1993) Combinatorial Enumeration. Wiley, New York.
 
[9]Pease, R.W. (1975) General Solution to the Occupancy Problem with Variably Sized Runs of Adjacent Cells Occupied by Single Balls. Mathematics Magazine, 48, 131-134.
http://dx.doi.org/10.2307/2689693
 
[10]Maosen, J. (1995) On Selecting k Balls from an n-Line or n-Circle without t-Separations. Northeastern Mathematical Journal, 11, 355-364.                                                                                       eww150108lx
标签：

评论

发表评论

此博客中的热门博文

Does Immigration Promote the Investment of the Monopolistic Firm?

In the present paper, we examine the effect of increasing uncertainty of immigrants’ growth on the optimal timing of investment of a firm that has a monopolistic power over the labor market. It is revealed that when the uncertainty of immigrants’ growth is more than a threshold level, increasing uncertainty of immigrants’ growth accelerates the optimal timing of firms’ investment and enhances the economic growth, even if the uncertainty of immigrants’ growth is formulated by the geometric Brownian motion, which is in sharp contrast to the standard result that an increase in the uncertainty postpones the optimal timing. With an increase in the immigrants over the past ten years, workforces in the host countries have been growing significantly to the extent that the immigrants represent 70% of the increase in the workforce in Europe, and 47% in the United States as OECD indicates. In the present paper, we attempted to investigate the effect of increased uncertainty caused by the growi...
发表评论
阅读全文

Education Policy Implementation: A Mechanism for Enhancing Primary Education Development in Zanzibar

Education is one of the fundamental rights of individuals; therefore, the government of a country needs to develop and strengthen educational policy and quality as well as to ensure that everyone has equal access to basic education. The improvement of access and quality of education in the world is becoming as an essential factor in development, whereas the basic education (primary school), is acknowledged as a foundation of the higher educational development for every country. To fulfill this goal, governments introduce several policies and procedures; however, it requires some reforms and participation from the politician, policymakers, and other stakeholders to re-examine educational policy so that it can lead to multiplication and betterment of the reforms. Educational reforms actually focus on accountability. A positive educational development and reform is very challenging and needs more effort and strategy on how to use and utilize the resources effectively as such it can achie...
发表评论
阅读全文