Graphical condensation for enumerating perfect matchings
نویسندگان
چکیده
The method of graphical condensation for enumerating perfect matchings was found by Propp (Theoretical Computer Science 303(2003), 267-301), and was generalized by Kuo (Theoretical Computer Science 319 (2004), 29-57). In this paper, we obtain some more general results on graphical condensation than Kuo’s. Our method is also different from Kuo’s. As applications of our results, we obtain a new proof of Stanley’s multivariate version of the Aztec diamond theorem and we enumerate perfect matchings of a type of molecular graph. Finally, a combinatorial identity on the number of plane partitions is also given.
منابع مشابه
Graphical condensation of plane graphs: A combinatorial approach
The method of graphical vertex-condensation for enumerating perfect matchings of plane bipartite graph was found by Propp (Theoret. Comput. Sci. 303(2003), 267-301), and was generalized by Kuo (Theoret. Comput. Sci. 319 (2004), 29-57) and Yan and Zhang (J. Combin. Theory Ser. A, 110(2005), 113125). In this paper, by a purely combinatorial method some explicit identities on graphical vertex-cond...
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A technique called graphical condensation is used to prove various combinatorial identities among numbers of (perfect) matchings of planar bipartite graphs and tilings of regions. Graphical condensation involves superimposing matchings of a graph onto matchings of a smaller subgraph, and then re-partitioning the united matching (actually a multigraph) into matchings of two other subgraphs, in o...
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 110 شماره
صفحات -
تاریخ انتشار 2005