彩色p元分区的算术性质

Pub Date : 2023-10-31 DOI:10.1007/s10474-023-01382-y

B. Żmija

{"title":"彩色p元分区的算术性质","authors":"B. Żmija","doi":"10.1007/s10474-023-01382-y","DOIUrl":null,"url":null,"abstract":"<div><p>We study divisibility properties of p-ary partitions colored with k(p − 1) colors for some positive integer k. In particular, we obtain a precise description of p-adic valuations in the case of <span>\\(k=p^{\\alpha}\\)</span> and <span>\\(k=p^{\\alpha}-1\\)</span>.</p><p>We also prove a general result concerning the case in which finitely many parts can be colored with a number of colors smaller than k(p − 1) and all others with exactly k(p − 1) colors, where k is arbitrary (but fixed).</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-023-01382-y.pdf","citationCount":"0","resultStr":"{\"title\":\"Arithmetic properties of colored p-ary partitions\",\"authors\":\"B. Żmija\",\"doi\":\"10.1007/s10474-023-01382-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study divisibility properties of p-ary partitions colored with k(p − 1) colors for some positive integer k. In particular, we obtain a precise description of p-adic valuations in the case of <span>\\\\(k=p^{\\\\alpha}\\\\)</span> and <span>\\\\(k=p^{\\\\alpha}-1\\\\)</span>.</p><p>We also prove a general result concerning the case in which finitely many parts can be colored with a number of colors smaller than k(p − 1) and all others with exactly k(p − 1) colors, where k is arbitrary (but fixed).</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10474-023-01382-y.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10474-023-01382-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-023-01382-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了k(p−1)色的p进分区的可整除性。特别地，我们得到了\(k=p^{\alpha}\)和\(k=p^{\alpha}-1\)情况下p进值的精确描述。我们还证明了关于有限多个部分可以用小于k(p−1)的颜色着色，而所有其他部分都可以用k(p−1)色着色的一般结果，其中k是任意的(但是固定的)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Arithmetic properties of colored p-ary partitions

We study divisibility properties of p-ary partitions colored with k(p − 1) colors for some positive integer k. In particular, we obtain a precise description of p-adic valuations in the case of \(k=p^{\alpha}\) and \(k=p^{\alpha}-1\).

We also prove a general result concerning the case in which finitely many parts can be colored with a number of colors smaller than k(p − 1) and all others with exactly k(p − 1) colors, where k is arbitrary (but fixed).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助