TY - JOUR
T1 - Spanning trees on two-dimensional lattices with more than one type of vertex
AU - Chang, Shu Chiuan
PY - 2009
Y1 - 2009
N2 - For a two-dimensional lattice Λ with n vertices, the number of spanning trees NST(Λ) grows asymptotically as exp(nz Λ) in the thermodynamic limit. We present an exact integral expression and a numerical value for the entropy (asymptotic growth constant) zΛ for spanning trees on 19 two-dimensional lattices with more than one type of vertex given in O'Keeffe and Hyde (1980 Philos. Trans. R. Soc. A 295 553). Especially, an exact closed-form expression for the entropy is derived for net 14, and the entropies of net 27 and the triangle lattice have the simple relation z27 = (ztri + ln 4)/4. Some integral identities are also obtained.
AB - For a two-dimensional lattice Λ with n vertices, the number of spanning trees NST(Λ) grows asymptotically as exp(nz Λ) in the thermodynamic limit. We present an exact integral expression and a numerical value for the entropy (asymptotic growth constant) zΛ for spanning trees on 19 two-dimensional lattices with more than one type of vertex given in O'Keeffe and Hyde (1980 Philos. Trans. R. Soc. A 295 553). Especially, an exact closed-form expression for the entropy is derived for net 14, and the entropies of net 27 and the triangle lattice have the simple relation z27 = (ztri + ln 4)/4. Some integral identities are also obtained.
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U2 - 10.1088/1751-8113/42/1/015208
DO - 10.1088/1751-8113/42/1/015208
M3 - Article
AN - SCOPUS:64549158841
SN - 1751-8113
VL - 42
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 1
M1 - 015208
ER -