The enumeration of several classes of hexagonal systems |
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| Authors: | Zhang Fuji Guo Xiaofeng |
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| Institution: | (1) Department of Mathematics, Xiamen University, 361005 Xiamen, China;(2) Institute of Mathematics and Physics, Xinjiang University, 830046 Wulumuqi, China |
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| Abstract: | In 1], we introduced the concept of z-transformation graphs of perfect matchings of hexagonal systems and showed that the z-transformation graph of perfect matchings of a hexagonal system has at most two vertices of degree one. In this paper, we enumerate the hexagonal systems whose z-transformation graphs have a vertex of degree one. In particular, such hexagonal systems with various symmetries are also enumerated. |
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| Keywords: | Hexagonal Systems z-transformation graphs generating functions partitions |
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