Abstract
Let L be a finite n-element semilattice. We prove that if L has at least 127 ⋅ 2n− 8 subsemilattices, then L is planar. For n > 8, this result is sharp since there is a non-planar semilattice with exactly 127 ⋅ 2n− 8 − 1 subsemilattices.
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FundRef: University of Szeged Open Access Fund, Grant number: 4450. Open access funding provided by University of Szeged (SZTE).
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This research was supported by the Hungarian Research, Development and Innovation Office under grant number KH 126581.
Dedicated to the memory of Ivo G. Rosenberg
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Czédli, G. One Hundred Twenty-Seven Subsemilattices and Planarity. Order 37, 559–569 (2020). https://doi.org/10.1007/s11083-019-09519-x
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DOI: https://doi.org/10.1007/s11083-019-09519-x