High-Dimensional Holeyominoes
نویسندگان
چکیده
What is the maximum number of holes enclosed by a $d$-dimensional polyomino built $n$ tiles? Represent this $f_d(n)$. Recent results show that $f_2(n)/n$ converges to $1/2$. We prove for all $d \geq 2$ we have $f_d(n)/n \to (d-1)/d$ as goes infinity. also construct polyominoes in tori with maximal possible per tile. In our proofs, use metaphors from error-correcting codes and dynamical systems.
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ژورنال
عنوان ژورنال: Electronic Journal of Combinatorics
سال: 2022
ISSN: ['1077-8926', '1097-1440']
DOI: https://doi.org/10.37236/10515