2005/09/15 by Weigen Yan, Yan, Weigen, Yeong-Nan Yeh +3
Mathematics · #05C70 #05C90 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C70 #msc:05C90
paper · pdf · doi:10.48550/arxiv.math/0509337
13 pages, 5 figures. accepted by Theoretial Computer Science
arxiv created 2005/09/23 · arxiv updated 2009/12/01
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), 113-125). In this paper, by a purely combinatorial method some explicit identities on graphical vertex-condensation for enumerating perfect matchings of plane graphs (which do not need to be bipartite) are obtained. As applications of our results, some results on graphical edge-condensation for enumerating perfect matchings are proved, and we count the sum of weights of perfect matchings of weighted Aztec diamond.