Pach, János and Tardos, Gábor (2024) Where Have All the Grasshoppers Gone? AMERICAN MATHEMATICAL MONTHLY, 131 (3). pp. 204-212. ISSN 0002-9890
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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 (Formula presented.). Some generalizations are also considered. © 2023 The Mathematical Association of America.
| Item Type: | Article |
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| Additional Information: | Export Date: 2 February 2024 Funding details: European Research Council, ERC Funding details: Hungarian Science Foundation Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFI, K-131529, K-132696 Funding text 1: We are grateful to Florestan Brunck for communicating this problem to us. The authors, together with him, posed the question on the 2022 Miklós Schweitzer Competition for Hungarian undergraduates and MSc students. This is arguably the most difficult mathematics contest of the world. The participants have 10 days to solve 10 problems []. This research was partially supported by the ERC advanced grants GeoScape and ERMID, and by the Hungarian Science Foundation (NKFIH) grants K-131529 and K-132696. Published online: 21 Dec 2023 WoS:hiba:001129455600001 2024-02-23 14:49 év nem egyezik |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 30 Mar 2024 10:57 |
| Last Modified: | 30 Mar 2024 10:57 |
| URI: | https://real.mtak.hu/id/eprint/191298 |
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