The Growth Constant of Odd Cutsets in High Dimensions-Reference-Cited by-同舟云学术

The Growth Constant of Odd Cutsets in High Dimensions

Published:2017-08-14 Issue:2 Volume:27 Page:208-227
ISSN:0963-5483
Container-title:Combinatorics, Probability and Computing
language:en
Short-container-title:Combinator. Probab. Comp.

Author:

FELDHEIM OHAD NOY,SPINKA YINON

Abstract

A cutset is a non-empty finite subset of ℤd which is both connected and co-connected. A cutset is odd if its vertex boundary lies in the odd bipartition class of ℤd. Peled [18] suggested that the number of odd cutsets which contain the origin and have n boundary edges may be of order eΘ(n/d) as d → ∞, much smaller than the number of general cutsets, which was shown by Lebowitz and Mazel [15] to be of order dΘ(n/d). In this paper, we verify this by showing that the number of such odd cutsets is (2+o(1))n/2d.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science

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