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%I #17 Oct 02 2023 13:45:07
%S 4,6,6,6,8,7,8,9,8,8,10,9,9,10,10,10,10,11,11,12,12,12,11,11,12,12,12,
%T 13,12,12,13,13,13,13,14,14,13,13,14,14,14,14,14,14,14,15,14,15,15,15,
%U 15,15,16,15,16,15,16,16,15,15,16,16,16,16,16,16,16,16,17,17,16,17,17,17,17,17
%N Quantitative (discrete) Helly numbers for the integer lattice Z^2.
%C a(n) = c(Z^2,n) is the smallest k>0 such that for every collection of convex sets C_1, ..., C_m having n points of Z^2 in common, there exists a subset of this collection of at most k elements such that they still contain exactly n points of Z^2 in common.
%C c(Z^2,n) = g(Z^2,n) = A298562(n) for n = 0, 1, ..., 200, but it is not known whether they agree for every n or not.
%H G. Averkov, B. González Merino, I. Paschke, M. Schymura, and S. Weltge, <a href="https://arxiv.org/abs/1602.07839">Tight bounds on discrete quantitative Helly numbers</a>, arXiv:1602.07839 [math.CO], 2016. See Fig. 3 p. 5.
%H G. Averkov, B. González Merino, I. Paschke, M. Schymura, and S. Weltge, <a href="https://doi.org/10.1016/j.aam.2017.04.003">Tight bounds on discrete quantitative Helly numbers</a>, Adv. in Appl. Math., 89 (2017), 76--101.
%F a(n) = max_{m=0..n} (A298562(m) + m - n). [Averkov et al.] - _Andrey Zabolotskiy_, Oct 02 2023
%Y Cf. A298562.
%K nonn
%O 0,1
%A _Bernardo González Merino_, Jan 26 2018
%E a(31) onwards from _Andrey Zabolotskiy_, Oct 02 2023
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