{"title":"关于数字段和平衡词的一些结果","authors":"Alessandro De Luca, Gabriele Fici","doi":"10.1016/j.tcs.2024.114935","DOIUrl":null,"url":null,"abstract":"<div><div>We exhibit combinatorial results on Christoffel words and binary balanced words that are motivated by their geometric interpretation as approximations of digital segments. We give a closed formula for counting the exact number of balanced words with <em>a</em> zeroes and <em>b</em> ones. We also study minimal non-balanced words.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1021 ","pages":"Article 114935"},"PeriodicalIF":0.9000,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some results on digital segments and balanced words\",\"authors\":\"Alessandro De Luca, Gabriele Fici\",\"doi\":\"10.1016/j.tcs.2024.114935\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We exhibit combinatorial results on Christoffel words and binary balanced words that are motivated by their geometric interpretation as approximations of digital segments. We give a closed formula for counting the exact number of balanced words with <em>a</em> zeroes and <em>b</em> ones. We also study minimal non-balanced words.</div></div>\",\"PeriodicalId\":49438,\"journal\":{\"name\":\"Theoretical Computer Science\",\"volume\":\"1021 \",\"pages\":\"Article 114935\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical Computer Science\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0304397524005528\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Computer Science","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304397524005528","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
摘要
我们展示了 Christoffel 词和二进制平衡词的组合结果，这些结果是由它们作为数字段近似值的几何解释所激发的。我们给出了一个封闭公式，用于计算有 a 个 0 和 b 个 1 的平衡词的精确数量。我们还研究了最小非平衡词。
Some results on digital segments and balanced words
We exhibit combinatorial results on Christoffel words and binary balanced words that are motivated by their geometric interpretation as approximations of digital segments. We give a closed formula for counting the exact number of balanced words with a zeroes and b ones. We also study minimal non-balanced words.
期刊介绍：
Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.
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