Faculty Profile

Dr Mohammad Salah Uddin

Associate Professor

Contact Information

  • Office Address: Department of Mathematics, Shahjalal University of Science and Technology, Sylhet-3114, Bangladesh
  • Phone: +8801911614515
  • Email: [email protected]

Research Profile Links

Biography

Dr. Mohammad Salah Uddin is best known for his significant contributions to enumerative combinatorics, particularly in the study of partially ordered sets (posets). He introduced the term “poset matrix” to describe the (0,1)-incidence matrix associated with poset structures and developed several innovative combinatorial interpretations of this concept. His work advances the computational understanding and provides new exact and algorithmic enumeration techniques that are relevant to combinatorics of graphs, posets, and lattices. His contributions continue to shape ongoing research and open new avenues in the study of ordered algebraic structures within combinatorics.

Dr. Mohammad Salah Uddin was born in 1981 in Satgaon, Chandina, Cumilla, and completed his SSC in 1996 from Gomta Ishakia High School and HSC in 1998 from Cumilla Victoria Government College. In 1999, he enrolled in the Department of Mathematics at Shahjalal University of Science and Technology (SUST), Sylhet, where he earned his BSc (Hons.) with a CGPA of 3.90 and MS (thesis) with a CGPA of 3.97 (out of 4.00), graduating top of his class in both programs. In 2008, Dr. Salah Uddin was awarded the prestigious UNESCO Fellowship to pursue a Postgraduate Diploma (PGD) in Mathematics, a pre-doctoral qualification, at the Abdus Salam International Centre for Theoretical Physics (ICTP) in Trieste, Italy, a globally recognized institute for advanced studies in mathematics and physics. He was also the recipient of the National Science and Technology (NST) Fellowship, awarded by the Ministry of Science and Technology, Government of Bangladesh, to support his doctoral studies in Mathematics for academic years 2017-18 to 2019–20.


Education

  • PhD in Mathematics, SUST, Sylhet, Bangladesh
  • PGD (Pre-PhD diploma) in Mathematics, ICTP, Trieste, Italy
  • MS (Thesis) (1st Position) in Mathematics, SUST, Sylhet, Bangladesh
  • BSc (Honors) (1st Position) in Mathematics, SUST, Sylhet, Bangladesh

Research Interests

  • Integer Sequences, MSC: 11Y55, 11-04
  • Enumerative Combinatorics, MSC: 05A15, 05-04, 05-08
  • Combinatorics of Posets (Partially Ordered Sets), MSC: 06A06, 06A07
  • Computational Aspects of Ordered Algebraic Structures, MSC: 06-04, 06-08

Active Research Project

  • 1. Matrix recognitions of several classes of lattices and their applications, SUST Research Center, PS/2025/1/22.

Previous Research Project

  • 1. Algebraic coding for secured data transmission, SUST Research Center, PS/2016/11.
  • 2. Theory of ordered sets as the generalization of lattice theory and its application to searching techniques, SUST Research Center, PS/2017/28.
  • 3. Algorithms for decomposing posets into terms and factors by using the poset matrix, SUST Research Center, PS/2018/1/09.
  • 4. Enumeration of n-element posets by using the poset matrix, SUST Research Center, PS/2019/1/20.
  • 5. Recognition of N-free posets by using the poset matrix and its application to enumeration, SUST Research Center, PS/2020/1/19.
  • 6. Recognition and enumeration of posets with bounded decomposition diameter, SUST Research Center, PS/2021/1/14.
  • 7. Recognition and enumeration of the unlabeled quasi-full t-ary rooted trees with n elements, where n>t≥2, SUST Research Center, PS/2022/1/20.
  • 8. Implementations of the matrix methods for combinatorial aspects of posets and lattices, SUST Research Center, PS/2023/1/19.
  • 9. Implementations of the matrix methods for combinatorial aspects of cyclic graphs, SUST Research Center, PS/2024/1/25.

External Affiliations

  • Life Member, Bangladesh Mathematical Society (AA-852).
  • Student Advisor, Dept. of Mathematics, SUST (Aug 2021 to Sep 2022).
  • Resource Person: MATLAB (Programming and Simulation) and Python (Numpy, Pandas, Matplotlib).
  • Developer of the Web App: Online Algebra Solution Engine (OASE), https://oase.daffodilvarsity.edu.bd.
  • Author of the Integer Sequences A349276, A349488, A350635 (P-series); A350772, A356558 (Series-parallel posets); A349367, A350783 (N-free posets); A352460 (Quasi-full rooted trees); and A379608 (Riordan posets) published in the Online Encyclopedia of Integer Sequences (OEIS), https://oeis.org.

Journal Publications

  • 1. S. U. Mohammad, M. S. Noor, and M. R. Talukder, Recognition and Enumeration of the Quasi-Full Rooted Trees, Journal of Integer Sequences, 28 (6) (2025), Article 25.6.3. (2025)
  • 2. S. U. Mohammad, M. R. Talukder, and S. N. Begum, Enumeration of unlabeled P-series by using the poset matrix, Asia Pacific Journal of Mathematics, 12 (2025), Article 68. (2025)
  • 3. S. U. Mohammad, M. R. Talukder, and S. N. Begum, Enumeration of unlabeled series-parallel posets by using the poset matrix, Palestine Journal of Mathematics, 14 (1) (2025), 217-232. (2025)
  • 4. S. U. Mohammad, M. S. Noor, and M. R. Talukder, Recognition of N-free posets by using the poset matrix, Asia Pacific Journal of Mathematics, 11 (2024), Article 72. (2024)
  • 5. S. U. Mohammad, M. R. Talukder, and S. N. Begum, Recognition of decomposable posets by using the poset matrix, Italian Journal of Pure and Applied Mathematics, 50 (2023), 455-466. (2023)
  • 6. S. U. Mohammad, M. S. Noor, and M. R. Talukder, An Exact Enumeration of the Unlabeled Disconnected Posets, Journal of Integer Sequences, 25 (5) (2022), Article 22.5.4. (2022)
  • 7. S. U. Mohammad and M. R. Talukder, Interpretations of Kronecker product and ordinal product of poset matrices, International Journal of Mathematics and Computer Science, 16 (4) (2021), 1665–1681. (2021)
  • 8. S. U. Mohammad and M. R. Talukder, Poset matrix and recognition of series-parallel posets, International Journal of Mathematics and Computer Science, 15 (1) (2020), 107-125. (2020)
  • 9. S. U. Mohammad, Computing dimension of affine varieties using Groebner basis approach, IOSR Journal of Mathematics, 8 (3) (2013), 36-39. (2013)

Conference

  • 1. S. U. Mohammad, M. N. Hoqe, and M. S. Noor, Computing finite binary Riordan matrices and their application to the enumeration of posets, 8th International Conference on Engineering Research, Innovation and Education (ICERIE) 2025, 24–26 April 2025, School of Applied Science and Technology, SUST, Sylhet, Bangladesh. (2025)
  • 2. S. U. Mohammad, D. Das, and M. R. Talukder, A Polynomial-Time Algorithm for Constructing Nondecreasing Integer Partitions and Its Application, Second Int. Conference on Mathematics and Applications (ICMA) 2024, 13-15 December 2024, Nepal Mathematics Society, Kathmandu, Nepal. (2024)
  • 3. S. U. Mohammad and M. S. Noor, Matrix recognition of the rooted trees and its application to enumeration, 1st International Conference in Physical Sciences (ICPS) 2022, 21-23 October 2022, School of Physical Science, SUST, Sylhet, Bangladesh. (2022)
  • 4. S. U. Mohammad, M. S. Noor, and M. R. Talukder, Recognition and enumeration of unlabeled N-free posets by using the poset matrix, 22nd International Mathematics Conference 2021, 10-11 December 2021, Bangladesh Mathematical Society (BMS), Bangladesh. (2021)
  • 5. S. U. Mohammad, M. R. Talukder, and S. N. Begum, Computing structural properties of finite posets, 5th International Conference on Engineering Research, Innovation and Education (ICERIE) 2019, 25-27 January 2019, School of Applied Science and Technology, SUST, Sylhet, Bangladesh. (2019)
  • 6. S. U. Mohammad and M. R. Talukder, Augmentation of poset matrices for sum and product of posets, 20th International Mathematics Conference 2017, 08-10 December 2017, Bangladesh Mathematical Society (BMS), Bangladesh. (2017)

Book/ Book Chapter

  • 1. S. U. Mohammad, Computational Algebraic Geometry and Groebner Basis: A Classical Introduction, Lambert Academic Publishing, Illustrated Edition, 2013.

Teaching

  • Linear and Abstract Algebra
  • Vector and Complex Analysis
  • Theory of Order and Lattices
  • Real Analysis and Adv. Real Analysis
  • Computational Algebraic Geometry
  • MATLAB, Python, and Mathematica

Awards & Recognition

  • Book Prize of the Convocation 2007 (for achieving the first position among all graduates of the year 2003), SUST.
  • Higher Education Scholarships (for achieving the first position among all graduates of the year 2003), UGC, Bangladesh.
  • Post Graduate Diploma Fellowship (for pre-PhD diploma in Mathematics) of the academic year 2008-09, The Abdus Salam ICTP, Trieste, Italy.
  • NST Fellowships (for doctoral studies in Mathematics) of the academic years 2017-18 to 2019-20, Ministry of Science and Technology, Bangladesh.

Graduate Supervision

  • 1. PhD: Current- 01
  • 2. MSc: Current- 03
  • 3. BSc: Former-07, Current- 03