Row-wise representation of arbitrary rhotrix

Chinedu M. Peter
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 18, 2012, Number 2, Pages 1–27
Full paper (PDF, 662 Kb)

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Authors and affiliations

Chinedu M. Peter
Department of Mathematics,
Ahmadu Bello University, Zaria, Nigeria

Abstract

We resolve two questions posed by Melvyn Nathanson, YangWang, and Alex Borisov concerning solutions with coefficients in ℚ of the functional equations arising from multiplication of quantum integers. First, we determine the necessary and sufficient criteria for determining when a rational function solution to these functional equations contains only polynomials. Second, we determine the sets of primes P for which there exist maximal solutions Γ_P to these functional equations with support bases P. We also give an explicit description of these maximal solutions.

Keywords

• Rhotrix
• Principal matrix
• Complementary matrix
• Inscribed matrix
• Row-wise representation
• Row-column multiplication
• Heart-oriented multiplication,
• Subrhotrix
• Submatrix

AMS Classification

• N/A

References

1. Ajibade, A. O., The Concept of Rhotrix in Mathematical Enrichment, International Journal of Mathematical Education in Science and Technology, Vol. 34, 2003, No. 2, 175–179.
2. Atanassov, K. T., A. G. Shannon, Matrix-tersions and Matrix-noitrets: Exercise in Mathematical Enrichment, Int. J. Math. Educ. Sci. Technol., Vol. 29, 1998, 898–903.
3. Ezugwu, E. A., B. Sani, J. B. Sahalu, The Concept of Heart Oriented Rhotrix Multiplication, GJSFR, Vol. 11, 2011, Issue 2, 35–46.
4. Kaurangini, M. L., B. Sani„ Hilbert Matrix and its Relationship with a Special Rhotrix,
   ABACUS (Journal of Mathematical Association of Nigeria), Vol. 34, 2007, No. 2A, 101–106.
5. Sani, B., An Alternative Method for Multiplication of Rhotrices, International Journal of Mathematics Education in Science and Technology, Vol. 35, 2004, No. 5, 777–781.
6. Sani, B., The row-column Multiplication of High Dimensional rhotrices, International Journal of Mathematical Education in Science and Technology, Vol. 38, 2007, 657–662
7. Sani, B., Solution of Two Coupled Matrices, The Journal of the Mathematical Association of Nigeria, Vol. 36, 2009, No. 2, 53–57.
8. Singh, D., C. M. Peter, Multiset-based Tree Model for Membrane Computing, Computer Science Journal of Moldova, Vol. 19, 2011, No. 1(55), 3–28.
9. Valpole, R. E., R. H. Myers, S. L. Myers, Probability and Statistics for Engineers and Scientists, Pearson Educational International, London, 2007.