Laurent phenomenon sequences
نویسندگان
چکیده
منابع مشابه
Laurent 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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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...
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We generalize Fomin and Zelevinsky’s cluster algebras by allowing exchange polynomials to be arbitrary irreducible polynomials, rather than binomials.
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Abstract. This paper is devoted to the study of asymptotic zero distribution of Laurent-type approximants under certain extremality conditions analogous to the condition of Grothmann [1], which can be traced back to Walsh’s theory of exact harmonic majorants [8, 9]. We also prove results on the convergence of ray sequences of Laurent-type approximants to a function analytic on the closure of a ...
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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...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2015
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-015-0647-5