The Laurent phenomenon

• Published in 2001
• Added on 2013-10-09

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 D.Gale and R.Robinson on integrality of generalized Somos sequences, and prove the Laurent property for several multidimensional recurrences, confirming conjectures by J.Propp, N.Elkies, and M.Kleber.

Links

• http://arxiv.org/abs/math.CO/0104241

Other information

BibTeX entry

@article{Fomin2001,
	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 D.Gale and R.Robinson on integrality of generalized Somos sequences, and prove the Laurent property for several multidimensional recurrences, confirming conjectures by J.Propp, N.Elkies, and M.Kleber.},
	author = {Fomin, Sergey and Zelevinsky, Andrei},
	month = {apr},
	pages = 21,
	title = {The Laurent phenomenon},
	url = {http://arxiv.org/abs/math.CO/0104241},
	year = 2001,
	urldate = {2013-10-09}
}