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• W2821770162 abstract "K. Adaricheva and M. Bolat have recently proved that if $U_0$ and $U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $U_{1-k}$ is included in the convex hull of $U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles. Here we prove the existence of such a $j$ and $k$ for the more general case where $U_0$ and $U_1$ are compact sets in the plane such that $U_1$ is obtained from $U_0$ by a positive homothety or by a translation. Also, we give a short survey to show how lattice theoretical antecedents, including a series of papers on planar semimodular lattices by G. Gratzer and E. Knapp, lead to our result." @default.
• W2821770162 created "2018-07-19" @default.
• W2821770162 creator A5070558748 @default.
• W2821770162 creator A5081174841 @default.
• W2821770162 date "2018-07-10" @default.
• W2821770162 modified "2023-09-27" @default.
• W2821770162 title "A convex combinatorial property of compact sets in the plane and its roots in lattice theory" @default.
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• W2821770162 hasPublicationYear "2018" @default.
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