On some classes of binary matrices

Krasimir Yordzhev
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 4, Pages 728–735
DOI: 10.7546/nntdm.2025.31.4.728-735
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Authors and affiliations

Krasimir Yordzhev
Trakia University, Stara Zagora, Yambol, Bulgaria

Abstract

The work considers the set \mathcal{L}_n^k of all n\times n binary matrices having the same number of k units in each row and each column. The article specifically focuses on the matrices whose rows and columns are sorted lexicographically. We examine some particular cases and special properties of this matrices. Finally, we demonstrate the relationship between the Fibonacci numbers and the cardinality of two classes of \mathcal{L}_n^k-matrices with lexicographically sorted rows and columns.

Keywords

  • Binary matrix
  • Sorted lexicographically
  • Decreasing order
  • Increasing order
  • Fibonacci numbers

2020 Mathematics Subject Classification

  • 15B34
  • 11B39

References

  1. Atanassov, K., Atanassova, V., Shannon, A., & Turner, J. (2002). New Visual Perspectives on Fibonacci Numbers. World Scientific, Singapore.
  2. Da Fonseca, C. M., & Saraiva, P. (2025). Some remarks on bivariate Mersenne–Lucas polynomials. Chaos, Solitons & Fractals, 200, Article ID 116901.
  3. Koshy, T. (2011). Fibonacci and Lucas Numbers with Applications. John Wiley & Sons.
  4. Tarakanov, V. E. (1972). Enumeration of stochastic cubes. Combinatorial Analysis, 5, 4–15 (in Russian).
  5. Yordzhev, K. (2013). On an algorithm for isomorphism-free generations of combinatorial objects. International Journal of Emerging Trends & Technology in Computer Science, 2(6), 215–220.
  6. Yordzhev, K. (2014) Factor-set of binary matrices and Fibonacci numbers. Applied Mathematics and Computation, 236, 235–238.
  7. The On-Line Encyclopedia of Integer Sequences. Available online at: https://oeis.org.

Manuscript history

  • Received: 21 July 2025
  • Revised: 21 September 2025
  • Accepted: 10 October 2025
  • Online First: 27 October 2025

Copyright information

Ⓒ 2025 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Yordzhev, K. (2025). On some classes of binary matrices. Notes on Number Theory and Discrete Mathematics, 31(4), 728-735, DOI: 10.7546/nntdm.2025.31.4.728-735.

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