Some exact results for spanning trees on lattices

Shu Chiuan Chang; Robert Shrock

doi:10.1088/0305-4470/39/20/001

Some exact results for spanning trees on lattices

Shu Chiuan Chang
, Robert Shrock

Institute for Theoretical Physics

National Cheng Kung University

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

For n-vertex, d-dimensional lattices Λ with d ≥ 2, the number of spanning trees N_ST(Λ) grows asymptotically as exp(nz _Λ) in the thermodynamic limit. We present an exact closed-form result for the asymptotic growth constant z_bcc(d) for spanning trees on the d-dimensional body-centred cubic lattice. We also give an exact integral expression for z_fcc on the face-centred cubic lattice and an exact closed-form expression for z₄₈₈ on the 4 8 8 lattice.

Original language	English
Pages (from-to)	5653-5658
Number of pages	6
Journal	Journal of Physics A: Mathematical and General
Volume	39
Issue number	20
DOIs	https://doi.org/10.1088/0305-4470/39/20/001
State	Published - May 19 2006

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title = "Some exact results for spanning trees on lattices",

abstract = "For n-vertex, d-dimensional lattices Λ with d ≥ 2, the number of spanning trees NST(Λ) grows asymptotically as exp(nz Λ) in the thermodynamic limit. We present an exact closed-form result for the asymptotic growth constant zbcc(d) for spanning trees on the d-dimensional body-centred cubic lattice. We also give an exact integral expression for zfcc on the face-centred cubic lattice and an exact closed-form expression for z488 on the 4 8 8 lattice.",

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N2 - For n-vertex, d-dimensional lattices Λ with d ≥ 2, the number of spanning trees NST(Λ) grows asymptotically as exp(nz Λ) in the thermodynamic limit. We present an exact closed-form result for the asymptotic growth constant zbcc(d) for spanning trees on the d-dimensional body-centred cubic lattice. We also give an exact integral expression for zfcc on the face-centred cubic lattice and an exact closed-form expression for z488 on the 4 8 8 lattice.

AB - For n-vertex, d-dimensional lattices Λ with d ≥ 2, the number of spanning trees NST(Λ) grows asymptotically as exp(nz Λ) in the thermodynamic limit. We present an exact closed-form result for the asymptotic growth constant zbcc(d) for spanning trees on the d-dimensional body-centred cubic lattice. We also give an exact integral expression for zfcc on the face-centred cubic lattice and an exact closed-form expression for z488 on the 4 8 8 lattice.

UR - https://www.scopus.com/pages/publications/33646399152

U2 - 10.1088/0305-4470/39/20/001

DO - 10.1088/0305-4470/39/20/001

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JO - Journal of Physics A: Mathematical and General

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Some exact results for spanning trees on lattices

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