Counting regions with bounded surface area
Abstract
Define a cubical complex to be a collection of integer-aligned unit cubes in d dimensions. Lebowitz and Mazel (1998) proved that there are between (C_1d)n/2d and (C_2d)64n/d complexes containing a fixed cube with connected boundary of (d - 1)-volume n. In this paper we narrow these bounds to between (C_3d)n/d and (C_4d)2n/d . We also show that there are n{n/(2d(d-1))+o(1) connected complexes containing a fixed cube with (not necessarily connected) boundary of volume n. © Springer-Verlag 2007.
Publication Title
Communications in Mathematical Physics
Recommended Citation
Balister, P., & Bollobás, B. (2007). Counting regions with bounded surface area. Communications in Mathematical Physics, 273 (2), 305-315. https://doi.org/10.1007/s00220-007-0231-5
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