TY - JOUR

T1 - The Growth Constant of Odd Cutsets in High Dimensions

AU - Feldheim, Ohad Noy

AU - Spinka, Yinon

N1 - Publisher Copyright:
© 2017 Cambridge University Press.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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 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.

AB - 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 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.

UR - http://www.scopus.com/inward/record.url?scp=85044286626&partnerID=8YFLogxK

U2 - 10.1017/S0963548317000438

DO - 10.1017/S0963548317000438

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AN - SCOPUS:85044286626

SN - 0963-5483

VL - 27

SP - 208

EP - 227

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

IS - 2

ER -