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- W4308668833 abstract "Let $P$ be an $N$-element point set in the plane. Consider $N$ (pointlike) grasshoppers sitting at different points of $P$. In a legal move, any one of them can jump over another, and land on its other side at exactly the same distance. After a finite number of legal moves, can the grasshoppers end up at a point set, similar to, but larger than $P$? We present a linear algebraic approach to answer this question. In particular, we solve a problem of Brunck by showing that the answer is yes if $P$ is the vertex set of a regular $N$-gon and $Nneq 3, 4, 6$. Some generalizations are also considered." @default.
- W4308668833 created "2022-11-14" @default.
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- W4308668833 date "2022-11-07" @default.
- W4308668833 modified "2023-10-06" @default.
- W4308668833 title "Where have all the grasshoppers gone?" @default.
- W4308668833 doi "https://doi.org/10.48550/arxiv.2211.03870" @default.
- W4308668833 hasPublicationYear "2022" @default.
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