Spanning Trees on the Sierpinski Gasket |
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| Authors: | Shu-Chiuan Chang Lung-Chi Chen Wei-Shih Yang |
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| Affiliation: | (1) Department of Physics, National Cheng Kung University, Tainan, 70101, Taiwan;(2) Physics Division, National Center for Theoretical Science, National Taiwan University, Taipei, 10617, Taiwan;(3) Department of Mathematics, Fu Jen Catholic University, Taipei, 24205, Taiwan;(4) Department of Mathematics, Temple University, Philadelphia, PA 19122, USA |
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| Abstract: | We present the numbers of spanning trees on the Sierpinski gasket SG d (n) at stage n with dimension d equal to two, three and four. The general expression for the number of spanning trees on SG d (n) with arbitrary d is conjectured. The numbers of spanning trees on the generalized Sierpinski gasket SG d,b (n) with d = 2 and b = 3,4 are also obtained. |
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| Keywords: | Spanning trees Sierpinski gasket exact solutions |
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