有向图的小马勒测度

IF 0.7 4区数学 Q2 MATHEMATICS

Experimental Mathematics Pub Date : 2021-10-16 DOI:10.1080/10586458.2021.1980462

Joshua Coyston, J. McKee

{"title":"有向图的小马勒测度","authors":"Joshua Coyston, J. McKee","doi":"10.1080/10586458.2021.1980462","DOIUrl":null,"url":null,"abstract":"Abstract We attach Mahler measures to digraphs and find combinatorial realizations of nearly all of the known low-degree ( ) small (< 1.3) one-variable Mahler measures. We find one new such measure not on either of the lists maintained by Mossinghoff and Sac-Épée. Considering limits of sequences of measures attached to families of digraphs, we get combinatorial explanations for 57 of the 61 known irreducible two-variable measures below 1.37.","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"32 1","pages":"527 - 539"},"PeriodicalIF":0.7000,"publicationDate":"2021-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Small Mahler Measures From Digraphs\",\"authors\":\"Joshua Coyston, J. McKee\",\"doi\":\"10.1080/10586458.2021.1980462\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We attach Mahler measures to digraphs and find combinatorial realizations of nearly all of the known low-degree ( ) small (< 1.3) one-variable Mahler measures. We find one new such measure not on either of the lists maintained by Mossinghoff and Sac-Épée. Considering limits of sequences of measures attached to families of digraphs, we get combinatorial explanations for 57 of the 61 known irreducible two-variable measures below 1.37.\",\"PeriodicalId\":50464,\"journal\":{\"name\":\"Experimental Mathematics\",\"volume\":\"32 1\",\"pages\":\"527 - 539\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-10-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Experimental Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/10586458.2021.1980462\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Experimental Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/10586458.2021.1980462","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们将马勒测度附加到有向图上，并找到了几乎所有已知的低次()小(< 1.3)单变量马勒测度的组合实现。我们在Mossinghoff和Sac维护的列表中发现了一个新的这样的度量-Épée。考虑有向图族所附测度序列的极限，我们得到了61个已知不可约双变量测度中57个小于1.37的组合解释。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Small Mahler Measures From Digraphs

Abstract We attach Mahler measures to digraphs and find combinatorial realizations of nearly all of the known low-degree ( ) small (< 1.3) one-variable Mahler measures. We find one new such measure not on either of the lists maintained by Mossinghoff and Sac-Épée. Considering limits of sequences of measures attached to families of digraphs, we get combinatorial explanations for 57 of the 61 known irreducible two-variable measures below 1.37.

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

来源期刊

Experimental Mathematics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses. Experiment has always been, and increasingly is, an important method of mathematical discovery. (Gauss declared that his way of arriving at mathematical truths was "through systematic experimentation.") Yet this tends to be concealed by the tradition of presenting only elegant, fully developed, and rigorous results. Experimental Mathematics was founded in the belief that theory and experiment feed on each other, and that the mathematical community stands to benefit from a more complete exposure to the experimental process. The early sharing of insights increases the possibility that they will lead to theorems: An interesting conjecture is often formulated by a researcher who lacks the techniques to formalize a proof, while those who have the techniques at their fingertips have been looking elsewhere. Even when the person who had the initial insight goes on to find a proof, a discussion of the heuristic process can be of help, or at least of interest, to other researchers. There is value not only in the discovery itself, but also in the road that leads to it.