TY - JOUR

T1 - On the widths of finite distributive lattices

AU - Kahn, Jeff

AU - Saks, Michael

N1 - Funding Information:
* Supported in part by NSF Grant MCS83-01867. * * Supported in part by a Sloan Research Fellowship.

PY - 1987

Y1 - 1987

N2 - The following conjecture of U Faigle and B Sands is proved: For every number R > 0 there exists a number n(R) such that if L is a finite distributive lattice whose width w(L) (size of the largest antichain) is at least n(R), then |L| ≥ Rw(L). In words this says that as one considers increasingly large distributive lattices, the maximum sized antichain contains a vanishingly small proportion of the elements.

AB - The following conjecture of U Faigle and B Sands is proved: For every number R > 0 there exists a number n(R) such that if L is a finite distributive lattice whose width w(L) (size of the largest antichain) is at least n(R), then |L| ≥ Rw(L). In words this says that as one considers increasingly large distributive lattices, the maximum sized antichain contains a vanishingly small proportion of the elements.

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U2 - 10.1016/0012-365X(87)90007-0

DO - 10.1016/0012-365X(87)90007-0

M3 - Article

AN - SCOPUS:38249036147

VL - 63

SP - 183

EP - 195

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 2-3

ER -