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 -