On a new generalization of Jacobsthal quaternions and several identities involving these numbers

• Autorzy: Bród Dorota , Szynal-Liana Anetta

Identyfikatory

DOI

10.14708/cm.v1-2i59.6492

• Języki publikacji: EN

Abstrakty

EN

In this paper we generalize Jacobsthal quaternions to (s, p) -Jacobsthal quaternions. We give some of their properties, among others the Binet formula, the generating function and the matrix representation of these quaternions. We will show how a graph interpretation can be used in proving some identities for quaternions.

Słowa kluczowe

EN

Jacobsthal numbers; Jacobsthal quaternions; recurrence relations; generating functions

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2019
• Tom: Vol. 59, No. 1/2
• Strony: 33--45
• Opis fizyczny: Bibliogr. 15 poz., rys.

Twórcy

autor

Bród Dorota

• Faculty of Mathematics and Applied Physics, Department of Discrete Mathematics, Rzeszow University of Technology, Powstańców Warszawy 12, 35-959 Rzeszów, Poland

autor

Szynal-Liana Anetta

• Faculty of Mathematics and Applied Physics, Department of Discrete Mathematics, Rzeszow University of Technology, Powstańców Warszawy 12, 35-959 Rzeszów, Poland

Bibliografia

• [1] F. T. Aydın and S. Yüce, A new approach to Jacobsthal quaternions, Filomat 31 (2017), no. 18, 5567-5579, DOI 10.2298/fil1718567t.
• [2] D. Bród, On a two-parameter generalization of Jacobsthal numbers and its graph interpretation, Ann. Univ. Mariae Curie-Skłodowska Sect. A LXXII (2018), no. 2, 21-28.
• [3] C. B. Çimen and A. İpek, On Pell quaternions and Pell-Lucas quaternions, Adv. Appl. Clifford Algebr. 26 (2016), no. 1, 39-51, DOI 10.1007/s00006-015-0571-8.
• [4] A. Dasdemir, The representation, generalized Binet formula and sums of the generalized Jacobsthal p-sequence, Hitite J. Sci. Eng. 3 (2016), no. 2, 99-104, DOI 10.17350/HJSE19030000038.
• [5] R. Diestel, Graph theory, Springer-Verlag, Heidelberg, New York 2005.
• [6] S. Falcon, On the k-Jacobsthal numbers, Am. Rev. Math. Stat. 2 (2014), no. 1, 67-77.
• [7] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Am. Math. Mon. 70 (1963), 289-291, DOI 10.2307/2313129.
• [8] A. F. Horadam, Quaternion recurrence relations, Ulam Quart. 2 (1993), 23-33.
• [9] D. Jhala, K. Sisodiya, and G. P. S. Rathore, On some identities for k-Jacobsthal numbers, Int. J. Math. Anal. (Ruse) 7 (2013), no. 12, 551-556, DOI 10.12988/ijma.2013.13052.
• [10] R. E. Merrifield and H. E. Simmons, Topological methods in chemistry, John Wiley & Sons, New York 1989.
• [11] A. Szynal-Liana and I. Włoch, A note on Jacobsthal quaternions, Adv. Appl. Clifford Algebr. 26 (2016), 441-447, DOI 10.1007/s00006-015-0622-1.
• [12] A. Szynal-Liana and I. Włoch, The Pell quaternions and the Pell octonions, Adv. Appl. Clifford Algebr. 26 (2016), 435-440, DOI 10.1007/s00006-015-0570-9.
• [13] D. Tasci, On k-Jacobsthal and k-Jacobsthal Lucas quaternions, J. Sci. Arts 3 (2017), no. 40, 469-476.
• [14] S. Uygun, Fe (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas sequences, Applied Mathematical Sciences 9 (2015), no. 70, 3467-3476, DOI 10.12988/ams.2015.52166.
• [15] J. P. Ward, Quaternions and Cayley numbers: algebra and applications, Kluwer Academic Publishers, London 1997.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).