FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
On the Laurent property of the Somos-8 sequences |
Bogoutdinova Yu.G. |
2019, issue 1, P. 6-9 |
Abstract |
| Zelevinsky and Fomin (2002) proved the Laurent property of the Somos-4, 5, 6, 7 sequences. In the paper the smallest number such that the corresponding element of the Somos-8 sequence is not a Laurent polynomial is calculated. |
Keywords: nonlinear recurrent sequences, quadratic sequences, Somos sequences |
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References |
| [1] S. Fomin, A. Zelevinsky, “The Laurent phenomenon”, Adv. Appl. Math., 28, (2002), 119–144. [2] M. Somos, “Problem 1470”, Crux Mathematicorum, 15, (1989), 208. [3] D. Gale, “The strange and surprising saga of the Somos sequences”, Math. Intelligencer, 13, (1991), 40–42. [4] J. L. Malouf, “An integer sequence from a rational recursion”, Discrete Mathematics, 110, (1992), 257–261. [5] J. Propp, “The Somos Sequence Site”, http://jamespropp.org/somos.html. |