Mathematics and Statistics Vol. 9(5), pp. 664 - 668
DOI: 10.13189/ms.2021.090506
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Starter Set Generation Based on Factorial Numbers for Half Wing of Butterfly Representation

Sharmila Karim ^*, Haslinda Ibrahim
Department of Mathematics & Statistics, School of Quantitative Sciences, Universiti Utara Malaysia, 06010 UUM Sintok, Kedah, Malaysia

ABSTRACT

Permutation is an interesting subject to explore until today where it is widely applied in many areas. This paper presents the use of factorial numbers for generating starter sets where starter sets are used for listing permutation. Previously starter sets are generated by using their permutation under exchange-based and cycling based. However, in the new algorithm, this process is replaced by factorial numbers. The base theory is there are number of distinct starter sets. Every permutation has its decimal number from zero until for Lexicographic order permutation only. From a decimal number, it will be converted to a factorial number. Then the factorial number will be mapped to its corresponding starter sets. After that, the Half Wing of Butterfly will be presented. The advantage of the use of factorial numbers is the avoidance of the recursive call function for starter set generation. In other words, any starter set can be generated by calling any decimal number. This new algorithm is still in the early stage and under development for the generation of the half wing of butterfly representation. Case n=5 is demonstrated for a new algorithm for lexicographic order permutation. In conclusion, this new development is only applicable for generating starter sets as a lexicographic order permutation due to factorial numbers is applicable for lexicographic order permutation.

KEYWORDS
Starter Sets, Factorial Numbers, Permutation, Half Wing of Butterfly Representation

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Sharmila Karim , Haslinda Ibrahim , "Starter Set Generation Based on Factorial Numbers for Half Wing of Butterfly Representation," Mathematics and Statistics, Vol. 9, No. 5, pp. 664 - 668, 2021. DOI: 10.13189/ms.2021.090506.

(b). APA Format:
Sharmila Karim , Haslinda Ibrahim (2021). Starter Set Generation Based on Factorial Numbers for Half Wing of Butterfly Representation. Mathematics and Statistics, 9(5), 664 - 668. DOI: 10.13189/ms.2021.090506.