Perfect matchings and the octahedron recurrence

DOI10.1007/s10801-006-0039-yzbMath1119.05092arXivmath/0402452OpenAlexW2038782505MaRDI QIDQ883148

Publication date: 31 May 2007

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402452

zbMATH Keywords

Aztec diamond Laurent polynomial Somos sequence Cluster algebra Perfect matching Octahedron recurrence

Mathematics Subject Classification ID

Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

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Cites Work