The Laurent phenomenon
Sergey Fomin, Andrei Zelevinsky
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.
Create a lesson
Related papers
Counting with Hiccup Sequences
Benoit Cloitre
Degree similar and net-degree similar signed graphs
Matteo Cavaleri, Alfredo Donno
Clique and chromatic numbers of graph powers: spectral bounds and anticodes
Aida Abiad, Gabriel Coutinho, Hitesh Kumar et al.
Counting cographs in locally dense graphs
Hyunwoo Lee
Two-orbit right-angled Polytopes and Hypertopes
Claudio Alexandre Piedade, Philippe Tranchida
On the failure of additivity of inversion numbers for dijoins
Natalie Behague, Jack Cromwell