The Laurent phenomenon
Combinatorics
2025-10-17 v1
Abstract
A composition of birational maps given by Laurent polynomials need not be given by Laurent polynomials; however, sometimes---quite unexpectedly---it does. We suggest a unified treatment of this phenomenon, which covers a large class of applications. In particular, we settle in the affirmative a conjecture of DGale and RRobinson on integrality of generalized Somos sequences, and prove the Laurent property for several multidimensional recurrences, confirming conjectures by JPropp, NElkies, and MKleber.
Cite
@article{arxiv.math/0104241,
title = {The Laurent phenomenon},
author = {Sergey Fomin and Andrei Zelevinsky},
journal= {arXiv preprint arXiv:math/0104241},
year = {2025}
}
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21 pages