References
- F.R.V. Alves, Bivariate Mersenne polynomials and matrices, Notes Number Theory Discrete Math. 26 (2020), no. 3, 83–95. DOI: 10.7546/nntdm.2020.26.3.83-95
- Ö. Arıbaş and M. Yıldız, On generalized commutative quaternions with generalized Tetranacci number components, Karaelmas Sci. Eng. J. 13 (2023), no. 2, 309–315.
- P. Catarino, H. Campos, and P. Vasco, On the Mersenne sequence, Ann. Math. Inform. 46 (2016), 37–53.
- W.R. Hamilton, Lectures on Quaternions, Hodges and Smith, Dublin, 1853.
- A.F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly 70 (1963), no. 3, 289–291.
- A.F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart. 3 (1965), no. 3, 161–176.
- A.F. Horadam and J.M. Mahon, Pell and Pell–Lucas polynomials, Fibonacci Quart. 23 (1985), no. 1, 7–20.
- T. Horzum and E.G. Kocer, On some properties of Horadam polynomials, Int. Math. Forum 4 (2009), no. 25–28, 1243–1252.
- A.L. Iakin, Generalized quaternions of higher order, Fibonacci Quart. 15 (1977), no. 4, 343–346.
- A.L. Iakin, Generalized quaternions with quaternion components, Fibonacci Quart. 15 (1977), no. 4, 350–352.
- M.R. Iyer, A note on Fibonacci quaternions, Fibonacci Quart. 7 (1969), no. 3, 225–229.
- M. Jafari and Y. Yayli, Generalized quaternions and their algebraic properties, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat. 64 (2015), no. 1, 15–27. DOI: 10.1501/commua10000000724
- B. Prasad, Generalized commutative p-Fibonacci quaternions, Math. Appl. (Warsaw) 52 (2024), no. 1, 119–136.
- N. Saba and A. Boussayoud, On the bivariate Mersenne Lucas polynomials and their properties, Chaos Solitons Fractals 146 (2021), Paper No. 110899, 6 pp. DOI: 10.1016/j.chaos.2021.110899
- A.M. Sergeev, Generalized Mersenne matrices and Balonin’s conjecture, Automat. Control and Computer Sci. 48 (2014), no. 4, 214–220. DOI: 10.3103/S0146411614040063
- E. Sevgi, The bivariate Horadam polynomials and hybrinomials, Authorea (2022), March 30, 8 pp. DOI: 10.22541/au.164864866.60338865/v1
- A. Szynal-Liana and I. Włoch, Generalized commutative quaternions of the Fibonacci type, Bol. Soc. Mat. Mex. (3) 28 (2022), no. 1, Paper No. 1, 9 pp. DOI: 10.1007/s40590-021-00386-4
- A. Szynal-Liana, I. Włoch, and M. Liana, Generalized commutative quaternion polynomials of the Fibonacci type, Ann. Univ. Mariae Curie-Skłodowska Sect. A 76 (2022), no. 2, 33–44. DOI: 10.17951/a.2022.76.2.33-44
- B. Yılmaz, N.G. Bilgin, and Y. Soykan, Generalized Pauli Fibonacci polynomial quaternions, Axioms 14 (2025), no. 6, Paper No. 449, 35 pp. DOI: 10.3390/axioms14060449