{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T06:32:23Z","timestamp":1760596343618,"version":"3.40.4"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T00:00:00Z","timestamp":1741305600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T00:00:00Z","timestamp":1741305600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Johannes Kepler University Linz"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2025,4]]},"abstract":"Abstract<\/jats:title>\n We prove that, for any \n \n $$B \\subset {\\mathbb {R}}$$<\/jats:tex-math>\n \n \n B<\/mml:mi>\n \u2282<\/mml:mo>\n R<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, the Cartesian product set \n \n $$B \\times B$$<\/jats:tex-math>\n \n \n B<\/mml:mi>\n \u00d7<\/mml:mo>\n B<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> determines \n \n $$\\Omega (|B|^{2+c})$$<\/jats:tex-math>\n \n \n \u03a9<\/mml:mi>\n (<\/mml:mo>\n |<\/mml:mo>\n B<\/mml:mi>\n \n |<\/mml:mo>\n \n 2<\/mml:mn>\n +<\/mml:mo>\n c<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> distinct angles.<\/jats:p>","DOI":"10.1007\/s00493-025-00135-5","type":"journal-article","created":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T10:35:51Z","timestamp":1741343751000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Lower Bound for the Number of Pinned Angles Determined by a Cartesian Product Set"],"prefix":"10.1007","volume":"45","author":[{"given":"Oliver","family":"Roche-Newton","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,7]]},"reference":[{"issue":"4","key":"135_CR1","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1007\/s00493-023-00035-6","volume":"43","author":"PJ Bradshaw","year":"2023","unstructured":"Bradshaw, P.J.: Growth in Sumsets of Higher Convex Functions. 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