# Integrality and the Laurent phenomenon for Somos 4 sequences

@article{Swart2005IntegralityAT, title={Integrality and the Laurent phenomenon for Somos 4 sequences}, author={Christine Swart and Andrew Hone}, journal={arXiv: Number Theory}, year={2005} }

Somos 4 sequences are a family of sequences defined by a fourthorder quadratic recurrence relation with constant coefficients. For particular choices of the coefficients and the four initial data,such recurrences can yield sequences of integers. Fomin and Zelevinsky have used the theory of cluster algebras to prove that these recurrences also provide one of the simplest examples of the Laurent phenomenon: all the terms of a Somos 4 sequence are Laurent polynomials in the initial data. The…

## 4 Citations

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