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103143 |
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|a Alman, Joshua
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|a Massachusetts Institute of Technology. Department of Mathematics
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|a Alman, Joshua
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|a Cuenca, Cesar A.
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|a Huang, Jiaoyang
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|a Cuenca, Cesar
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|a Huang, Jiaoyang
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|a Cuenca, Cesar A.
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|a Laurent phenomenon sequences
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|b Springer US,
|c 2016-06-17T17:20:38Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/103143
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|a In this paper, we undertake a systematic study of sequences generated by recurrences x[subscript m+n]x[subscript m]=P(x[subscript m+1],...,x[subscript m+n−1])xm+nxm=P(xm+1,...,xm+n−1) which exhibit the Laurent phenomenon. Some of the most famous among these are the Somos and the Gale-Robinson sequences. 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 seeds in the cases of n=2,3 and of mutual binomial seeds. We also find several other interesting families of polynomials P whose generated sequences exhibit the Laurent phenomenon. Our classification for binomial seeds is a direct generalization of a result by Fordy and Marsh, that employs a new combinatorial gadget we call a double quiver.
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|a National Science Foundation (U.S.) (grants DMS-1067183 and DMS-1148634)
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|a Article
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|t Journal of Algebraic Combinatorics
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