Affine Magic Cubes of Order 4: Concepts and Applications

Int. J. Math. Math. Sci. Pub Date : 2022-10-26 DOI:10.1155/2022/2578562

Siriyakorn Duangmoon, Praphon Kanokladarom, Suchada Pongprasert, T. Rungratgasame, Natsima Srithaisong

{"title":"Affine Magic Cubes of Order 4: Concepts and Applications","authors":"Siriyakorn Duangmoon, Praphon Kanokladarom, Suchada Pongprasert, T. Rungratgasame, Natsima Srithaisong","doi":"10.1155/2022/2578562","DOIUrl":null,"url":null,"abstract":"We convert a classical magic cube of order 4, which is an arrangement of \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <mfenced open=\"{\" close=\"}\" separators=\"|\">\n <mrow>\n <mn>1,2</mn>\n <mo>,</mo>\n <mo>…</mo>\n <mo>,</mo>\n <mn>64</mn>\n </mrow>\n </mfenced>\n </math>\n , to a cube of order 4 whose entries belong to \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\n <msubsup>\n <mi>F</mi>\n <mn>2</mn>\n <mn>6</mn>\n </msubsup>\n </math>\n . By using finite-dimensional vector spaces over the field \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\n <msub>\n <mrow>\n <mi>F</mi>\n </mrow>\n <mrow>\n <mn>2</mn>\n </mrow>\n </msub>\n </math>\n , we introduce the notion of affine magic cubes and study their properties. The obtained results can be applied to describe some features of various types of magic cubes of order 4.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Math. Math. Sci.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2022/2578562","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

Abstract

We convert a classical magic cube of order 4, which is an arrangement of

\{1,2, \dots, 64\}

, to a cube of order 4 whose entries belong to

F_{2}^{6}

. By using finite-dimensional vector spaces over the field

F_{2}

, we introduce the notion of affine magic cubes and study their properties. The obtained results can be applied to describe some features of various types of magic cubes of order 4.

查看原文