{"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}
引用次数: 0
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.
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.
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