The Laurent Phenomenon
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.
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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...
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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 a semi-norm for the Alexander polynomial of a connected, compact, oriented 3-manifold on its first cohomology group to a seminorm for an arbitrary Laurent polynomial f on the dual vector space to the space of exponents of f . We determine a decomposition formula for this Laurent norm; an expression for the Laurent norm for f in terms of the Laurent norms for each of the irreducibl...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2002
ISSN: 0196-8858
DOI: 10.1006/aama.2001.0770