List of Selected Publications

1. Ibrahim M., Ibrahim A.A., Yakubu M.A.and Danzaki K.M (2012) Algebraic Theoretic Propeties of the (132)-avoiding Class of Aunu Permutation Patterns; Applications in Eulerian Graphs. Journal of Sciences and Technology Researh 11 (2) 90-95.

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2. Ibrahim M., Ibrahim A.A. and G.A. Isa (2012) Algebraic Theoretic Propeties of the (132)- avoiding Class of Aunu Permutation Patterns; Applications in Graphs. International Journal of Mathematical and Computational Analysis 4 (1) 48-55.

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3. Ibrahim M., Abubakar I., M.I. Iliyasu and Zubairu A. (2012) Algebraic Theoretic Propeties of the (123) and (132)-avoiding Class of Aunu Permutation Patterns; Applications in Eulerian Graphs. International Journal of Research and Advancement in physical science 2(1) 90-98.

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4. Ibrahim M., Ibrahim A.A.,Aminu M.K.and Aliyu M.L.(2012) Algebraic Theoretic Propeties of the (132)-avoiding Class of Aunu Permutation Patterns; Applications in Partially ordered set . African of physical sciences 5(2)106-109

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5. Ibrahim M., Shehu S.A., M.B. Abubakar, M.I. Iliyasu (2012) Algebraic Theoretic Propeties of the (123) and (132)-avoiding Class of Aunu Permutation Patterns; Applications in Partially ordered set . International Journal of Advancement in physical science 4(3) 81-84.

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6. Zubairu A. and Ibrahim M. (2012) Construction of quaternion group as a semi direct-product. African journal of physical sciences. 5(1) 54-62.

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7. Ibrahim M., Ibrahim A.A. and Magami M.S (2014) On block Design and the special class of (123)-avoiding Aunu Permutation Pattern; A Slanted Flag Model. International Organization of scientific Research journal of Mathematics. 10(3) 54-57.

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8. Magami M.S., Ibrahim A.A, Garba I.A., Usman A. and Ibrahim M. (2015) An Analysis of Group theoretic properties of a Class (123)-avoiding patterns of Aunu numbers using thin Cyclic design Proceedings of Annual National Conference of Mathematical Association of Nigeria (MAN): 92-96.

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9. H.Usman, M.S.Magami, M.Ibrahim and E.Omokhuale (2017) Combined effect of Magnetic Field and Chemical relation on unsteady natural convective flow in a Vertical porous channel. Asian Journal of Mathematics and Computer Research: 87-100. (Index at EBSCOhost)

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10. Ibrahim M., Ibrahim A.A., Garba A.I. and Aremu K.O. (2017) Ascent on non-deranged Permutation Group .International Journal of Science for Global Sustainability: 27-32.

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11. Ibrahim M.and A.I. Garba (2018) Excedance on -non deranged Permutations . Proceedings of Annual National Conference of Mathematical Association of Nigeria (MAN) National Secretariat, Kwali Abuja.

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12. Kazeem Olakekan Aremu, Rabiu Aliyu Abdulmimin, Muhammad Ibrahim and Jamilu Abubakar (2018), Some Result Associated with the Diagonal of Derived Plane Permutation ,Punjab University Journal of Mathematics 51(1) 9-15. (Index at EBSCO, Google Scholar e.t.c)

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13. Ibrahim M. and Garba A.I. (2019), Descent on non-deranged Permutation Group, Journal of the Mathematical Association of Nigeria (ABACUS), 46(1) 12-18.

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14. Garba A.I. and Ibrahim M. (2019), Inversion and Major index on non-deranged Permutations International Journal of Research and Innovation in Applied Science,4(10):119-123. (Index at Google Scholar, Academia.com e.t.c)

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15. Ibrahim M. and Garba A.I. and (2019). Motzkin Paths and Motzkin Polynomials of non-deranged Permutations ,International Journal of Research and Innovation in Applied Science,4(11):119-123. (Index at Google Scholar, Academia.com e.t.c)

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16. M. Ibrahim and M. Muhammad (2019). Standard Representation of set partition of -non deranged permutations, International Journal of Computer Science and Engineering, 7(11):79-84. Doi:https://doi.org/10.26438/ijcse/v7i11.7984

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17. Ibrahim,M. and M.S.Magami(2019). Onfixed decomposition of - non deranged permutations International Journal of Scientific and Research Publications 9(12) 158-162. Doi:10.29322/IJSRP.9.12.2019.p9620

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18. Ibrahim, M. and Ibrahim, B.A.(2019). Permutation Graphs with Inversion on --non deranged permutations IOSR Journal of the Mathematics,15(6):77-81. Doi :10.9790/5728-1506057781

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19. M.S. Magami and Ibrahim M. (2021) Partition Block Coordinate Statistics on -non deranged Permutations . Quest Journal of Research in Applied Mathematics, 7(9):28- 33. (Index at Google Scholar, Crossref e.t.c)

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20. M.S. Magami and Ibrahim M. (2021) Admissible Inversion on -non deranged Permutations . Asian Research Journal of Mathematics, 17(8):44-53. Doi : 10.9734/ARJOM/2021/v17i830322

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21. B.A.Buhari, Ibrahim M. and Ibrahim, A,A.(2021) First segment on Homology Computation for a class of ( 123)- avoiding pattern of Aunu permutation Proceedings of Annual National Conference of Mathematical Association of Nigeria (MAN): 89-96.

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22. B.A.Buhari, Ibrahim M. and Ibrahim, A,A.(2021) Second segment on Homology Computation for a class of ( 123)- avoiding pattern of Aunu permutation Quest Journal of Research in Applied Mathematics, 7(10):15- 23 . (Index at Google Scholar, Crossref e.t.c)

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23. Ibrahim, A,A, Ibrahim M. and B.A.Buhari (2022). Embracing sum using Ascent block of Γ1-deranged Permutations. International Journal of Advances in Engineering and Management,4(5),272-277. Doi:35629/5252-0405272277.

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G.

List of Published Books (Please provide titles, Name of Publishers, URL links and ISBN number)

a) Ibrahim, A.A., Uwanta,I.J., Ali, U.A., Isa, G.A.,Kamba, S.A.,Ibrahim, Z., Ibrahim, M., Abubakar,S.I. and Shehu, S., (2013), Topics in Introductory University Mathematics 1,ISBN:978-978-937-052-8,Ibro Business Centre,Sokoto.

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b) Aminu A. Ibrahim, Zaid Ibrahim, Ibrahim Muhammad,A.M.Dogondaji, Buhari Auwalu and M.S.Magami (2016), Pratical Lessons for Teaching of Algebraic Operations to Primary SchoolPupils,ISBN:978-978-941-008-8, Alley Graphic Printers ,Kaduna.

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c) Aminu A. Ibrahim, Zaid Ibrahim,Ibrahim Muhammad,A.M.Dogondaji,Buhari Auwalu and M.S.Magami (2016), Pratical Lessons in the Teaching of Geometry for Secondary School,ISBN:978-978-941-009-5,Alley Graphic Printers, Kaduna.

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d) Ibrahim A.A, and Ibrahim M. (2021) Introduction To Graph Theory, ISBN: 978-978-997-112-1, Usmanu Danfodiyo University press, Sokoto.

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Google Scholar: https://scholar.google.com/citations?user=HzSE5LIAAAAJ&hl=en

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LinkedIn ID: https://www.linkedin.com/in/ibrahim-muhammad-a01ba4128

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ORCID- https//orcid.org/000-0003-2503-9617