combinatorics / Extremal Combinatorics, Covering Problems
For $A=\{0,1,2\}^d$, write $f(d)$ for the fewest proper sub-boxes covering every point exactly twice. Leader, Miličević and Tan asked whether $f(d)\ge 2^d$ for all $d$, as Question 4.1 of the PatternBoost paper. The paper gives new bounds on $f(d)$.
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Improved bounds rather than a settled question: the asked-for inequality is not established in general.
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For $A=\{0,1,2\}^d$, write $f(d)$ for the fewest proper sub-boxes covering every point exactly twice. Leader, Miličević and Tan asked whether $f(d)\ge 2^d$ for all $d$, as Question 4.1 of the PatternBoost paper. The paper gives new bounds on $f(d)$.
Improved bounds rather than a settled question: the asked-for inequality is not established in general.
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