{"title":"A Lower Bound for the Number of Pinned Angles Determined by a Cartesian Product Set","authors":"Oliver Roche-Newton","doi":"10.1007/s00493-025-00135-5","DOIUrl":null,"url":null,"abstract":"<p>We prove that, for any <span>\\(B \\subset {\\mathbb {R}}\\)</span>, the Cartesian product set <span>\\(B \\times B\\)</span> determines <span>\\(\\Omega (|B|^{2+c})\\)</span> distinct angles.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"53 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Combinatorica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00493-025-00135-5","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove that, for any \(B \subset {\mathbb {R}}\), the Cartesian product set \(B \times B\) determines \(\Omega (|B|^{2+c})\) distinct angles.
期刊介绍:
COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are
- Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups).
- Combinatorial optimization.
- Combinatorial aspects of geometry and number theory.
- Algorithms in combinatorics and related fields.
- Computational complexity theory.
- Randomization and explicit construction in combinatorics and algorithms.