The Growth Constant of Odd Cutsets in High Dimensions

Ohad Noy Feldheim; Yinon Spinka

doi:10.1017/S0963548317000438

The Growth Constant of Odd Cutsets in High Dimensions

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

Abstract

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

Original language	English
Pages (from-to)	208-227
Number of pages	20
Journal	Combinatorics Probability and Computing
Volume	27
Issue number	2
DOIs	https://doi.org/10.1017/S0963548317000438
State	Published - 1 Mar 2018
Externally published	Yes

Bibliographical note

Funding Information:
Research of Y.S. supported by Israeli Science Foundation grant 861/15, the European Research Council starting grant 678520 (LocalOrder), and the Adams Fellowship Program of the Israel Academy of Sciences and Humanities.

Publisher Copyright:
© 2017 Cambridge University Press.

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The Growth Constant of Odd Cutsets in High Dimensions

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