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Codes Cryptogr."],"published-print":{"date-parts":[[2025,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>We characterize the permutations of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathbb {F}_q$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>F<\/mml:mi>\n                    <mml:mi>q<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> whose graph minimizes the number of collinear triples and describe the lexicographically-least one, confirming a conjecture of Cooper-Solymosi. This question is connected to Dudeney\u2019s No-3-in-a-Line problem, the Heilbronn triangle problem, and the structure of finite plane Kakeya sets. We discuss a connection with complete sets of mutually orthogonal latin squares and state a few open problems primarily about general finite affine planes.<\/jats:p>","DOI":"10.1007\/s10623-025-01632-w","type":"journal-article","created":{"date-parts":[[2025,4,23]],"date-time":"2025-04-23T11:32:23Z","timestamp":1745407943000},"page":"3135-3142","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Permutations minimizing the number of collinear triples"],"prefix":"10.1007","volume":"93","author":[{"given":"Joshua","family":"Cooper","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jack","family":"Hyatt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,4,23]]},"reference":[{"key":"1632_CR1","series-title":"Bolyai Soc. Math. 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