caa a22 4500 445855533 CHVBK 20180317145427.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00026-011-0088-3 doi (NATIONALLICENCE)springer-10.1007/s00026-011-0088-3 Musiker Gregg Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 02139, Cambridge, MA, USA aut A Graph Theoretic Expansion Formula for Cluster Algebras of Classical Type [Elektronische Daten] [Gregg Musiker] In this paper we give a graph theoretic combinatorial interpretation for the cluster variables that arise in most cluster algebras of finite type with bipartite seed. In particular, we provide a family of graphs such that a weighted enumeration of their perfect matchings encodes the numerator of the associated Laurent polynomial while decompositions of the graphs correspond to the denominator. This complements recent work by Schiffler and Carroll-Price for a cluster expansion formula for the A n case while providing a novel interpretation for the B n, C n, and D n cases. Springer Basel AG, 2011 cluster algebras nationallicence classical type nationallicence perfect matchings nationallicence laurentness nationallicence Annals of Combinatorics SP Birkhäuser Verlag Basel 15/1(2011-03-01), 147-184 0218-0006 15:1<147 2011 15 26 https://doi.org/10.1007/s00026-011-0088-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00026-011-0088-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Musiker Gregg Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 02139, Cambridge, MA, USA aut NATIONALLICENCE 773 0- Annals of Combinatorics SP Birkhäuser Verlag Basel 15/1(2011-03-01), 147-184 0218-0006 15:1<147 2011 15 26 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer