
TL;DR
This paper explores Nurikabe puzzles on non-orientable surfaces like Möbius strips and Klein bottles, establishing new combinatorial connections and proposing two variants of the puzzle.
Contribution
It introduces two versions of non-orientable Nurikabe and investigates their combinatorics on various non-orientable surfaces.
Findings
Established connections with OEIS sequences A101946, A213387, A123203, and A001045.
Analyzed combinatorics of non-orientable Nurikabe on different surfaces.
Proposed two variants of Nurikabe for non-orientable surfaces.
Abstract
We study Nurikabe puzzles on non-orientable surfaces. Specifically, we propose two versions of non-orientable Nurikabe and investigate their combinatorics on M\"obius strips, Klein bottles, and projective planes of size . Our results establish new connections among the OEIS sequences A101946, A213387, A123203, and A001045 (the Jacobsthal sequence).
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Taxonomy
TopicsGenetic Neurodegenerative Diseases
