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| Formato: | Preprint |
| Publicado: |
2001
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| Acceso en liña: | https://arxiv.org/abs/math/0104241 |
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| _version_ | 1866917019858763776 |
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| author | Fomin, Sergey Zelevinsky, Andrei |
| author_facet | Fomin, Sergey Zelevinsky, Andrei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0104241 |
| institution | arXiv |
| publishDate | 2001 |
| record_format | arxiv |
| spellingShingle | The Laurent phenomenon Fomin, Sergey Zelevinsky, Andrei Combinatorics 14E05 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. |
| title | The Laurent phenomenon |
| topic | Combinatorics 14E05 |
| url | https://arxiv.org/abs/math/0104241 |