Generalization of Some Problems with s-Separation ()
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.
Share and Cite:
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.
Conflicts of Interest
The authors declare no conflicts of interest.
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.
|