ON SOME NON-DERANGED PERMUTATION: A NEW METHOD OF CONSTRUCTION

Suleiman I; Garba A.I; Mustafa A

doi:10.29121/granthaalayah.v8.i3.2020.162

Authors

Suleiman I Department of Mathematics, Usmanu Danfodiyo University, Sokoto, P.M.B 2346 Sokoto, Nigeria
Garba A.I Department of Mathematics, Usmanu Danfodiyo University, Sokoto, P.M.B 2346 Sokoto, Nigeria
Mustafa A Department of Mathematics, Usmanu Danfodiyo University, Sokoto, P.M.B 2346 Sokoto, Nigeria

DOI:

https://doi.org/10.29121/granthaalayah.v8.i3.2020.162

Keywords:

Permutation, Aunu permutation ω_i and Group

Abstract [English]

In this paper, we construct a permutation group via a composition operation on some permutations generated from the structure for prime and as defined by [1]. Thus, providing a new method of constructing permutation group from existing ones.

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References

Suleiman I, Ibrahim A. A and Ejima O. (2019). On the Addition Modulus of the Aunu Pattern ω_i∈ G_p: An Investigation of Some Topological Properties. J Phys Math 10: 299.

Sam Miner and Igor Park, (2013). The Shape of Random Pattern-avoiding Permutations. Journal of Advances in Applied Mathematics. Vol. 55, 86 -130.

Miklo’s Bona (2012), Surprising Symmetries in Objects Counted by Catalan Numbers. The Electronic Journal of Combinatorics, 19, #p62.

Desantis D., Field R., Hough W., Jones B., Meissen R., Ziefle J., (2000). Permutations, Pattern Avoidance, and the Catalan Triangle. Retrieved from

http://educ.jmu.edu/~jones3bc/catalanmjms.pdf.

Abba S., A.A Ibrahim and B.A Madu (2015), Some Applications of Special 123-avoiding/132-avoiding Permutations to Combinatorics. Kastina Journal of National and Applied Science. Vol.4, No.1

Garba A.I and Ibrahim A.A. (2009). A New Method Of Constructing A Variety Of Finite Group Based On Some Succession Scheme. Proceeding of International Conference on Research and Development. 2. 16.

Usman A. and Ibrahim A.A. (2011). A New Generating Function for Aunu Patterns: Application in Integer Group modulo n. Nigerian Journal of Basics and Applied Science. 19(1):1 -4.

Ibrahim A.A (2007). An Enumeration Scheme on Some Algebraic Properties of a Special (132)-avoiding Class of Permutation Pattern. Trend in Applied Research. 2(4), 334-340. DOI: https://doi.org/10.3923/tasr.2007.334.340

Abba, S., and Ibrahim, A.A., (2014). On Comparison of Aunu permutation pattern and generalized permutation patterns using Wilf-equivalence. Mathematical Theory and Modeling. 4,5.

Abubakar, S.I, Shehu, S., Zaid, I., and Ibrahim, A.A., (2014). Some Polynomial Representation Using the 123-avoiding class of the Aunu Permutation Pattern of Cardinality Five Using Binary Codes. International Journal of Science and Engineering Research. Vol.5, Issues 8.

Aremu, K.O., Ibrahim, A.H., Buoro, S., and Akinola, F.A. (2017). Pattern Popularity in Γ_1 -Non deranged Permutation: An algebraic and Algorithmic Aproach. Anale.Seria Infomatica. Vol.XV fasc 2. 115-122.

Usman, A., and Magami, M.S., (2015). An Analysis of Group Theoretic Properties of a Class of (123)-avoiding pattern of Aunu Number using Thin Cycle Design. Mathematical Theory and Modelling. Vol.5, No 5.

Chun, P.B., Ibrahim, A.A,. and Garba, A.I., (2016). Algebraic Theoretic Properties of the Non-associative Class of (132)-Avoiding Patterns of Aunu Permutations: Applications in the Generation and Analysis of a General Cyclic Code. Computer Science and Information Technology. 4(2): 45-47.

Ibrahim, A.A, Ejima O., and Kazeem O.A. (2016). On the Representations of Γ_1 -Nonderanged Permutation Group G_p . Advances in Pure Mathematics. 6, 608-614. DOI: https://doi.org/10.4236/apm.2016.69049

Garba, A.I., Ejima, O., Aremu, K.O., and Usman, H., (2017). Non-Standard Young Tableaux of Γ_1 Non-deranged Permutation Group G_p^( Γ_1 ). Global Journal of Mathematical Analysis. 5(1) 21-23.

Garba, A.I., Yusuf, A., and Hassan, A., (2018). Some Topological Properties of a Constructed Structure. Journal of the Nigerian Association of Mathematical Physics. Vol.45, 21-26.

Garba, A.I, Mustafa, A. and Suleiman, I. (2019). On Some Permutation Statistics of the Aunu Pattern ω_i∈ G_p. Annals Computer Science Series. Vol. XVII. Fasc-2. 36-38.