Laurent phenomenon algebras
نویسندگان
چکیده
منابع مشابه
Laurent phenomenon algebras
We generalize Fomin and Zelevinsky’s cluster algebras by allowing exchange polynomials to be arbitrary irreducible polynomials, rather than binomials.
متن کاملLaurent Phenomenon Sequences
In this paper, we undertake a systematic study of recurrences xm+nxm = P (xm+1, . . . , xm+n−1) which exhibit the Laurent phenomenon. Some of the most famous among these sequences come from the Somos and the Gale-Robinson recurrences. Our approach is based on finding period 1 seeds of Laurent phenomenon algebras of Lam-Pylyavskyy. We completely classify polynomials P that generate period 1 seed...
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Type A, or Ptolemy cluster algebras are a prototypical example of finite type cluster algebras, as introduced by Fomin and Zelevinsky. Their combinatorics is that of triangulations of a polygon. Lam and Pylyavskyy have introduced a generalization of cluster algebras where the exchange polynomials are not necessarily binomial, called Laurent phenomenon algebras. It is an interesting and hard que...
متن کاملIntegrality and the Laurent phenomenon for Somos 4 sequences
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...
متن کاملLaurent Keller
Laurent Keller is a professor at the University of Lausanne, where he directs the Department of Ecology and Evolution. After his PhD in Lausanne, he completed a postdoc with E.O. Wilson at Harvard and then returned to Bern and Lausanne with a special research and teaching grant from the Swiss NSF. He then applied with Nicolas Perrin to share a chair in the Department of Ecology in Lausanne; fol...
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ژورنال
عنوان ژورنال: Cambridge Journal of Mathematics
سال: 2016
ISSN: 2168-0930,2168-0949
DOI: 10.4310/cjm.2016.v4.n1.a2