{"title":"序列针织","authors":"S. Jensen","doi":"10.1080/17513472.2023.2199375","DOIUrl":null,"url":null,"abstract":"Sequence knitting comes from a straightforward directive; determine a short basic sequence of stitches and create a piece by continuous repetition of that sequence. This paper determines the number of sequence knitting patterns. We restrict our attention to sequences containing only knit and purl stitches and to flat knitting. We further assume that a sequence is restarted at the beginning of each row of knitting, but we do not assume that the number of stitches cast on is a multiple of the sequence length. We consider the case that a pattern and its left/right mirror image are the same, and the case that a pattern and its left/right mirror image are not necessarily the same. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"18 1","pages":"111 - 139"},"PeriodicalIF":0.3000,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sequence knitting\",\"authors\":\"S. Jensen\",\"doi\":\"10.1080/17513472.2023.2199375\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Sequence knitting comes from a straightforward directive; determine a short basic sequence of stitches and create a piece by continuous repetition of that sequence. This paper determines the number of sequence knitting patterns. We restrict our attention to sequences containing only knit and purl stitches and to flat knitting. We further assume that a sequence is restarted at the beginning of each row of knitting, but we do not assume that the number of stitches cast on is a multiple of the sequence length. We consider the case that a pattern and its left/right mirror image are the same, and the case that a pattern and its left/right mirror image are not necessarily the same. GRAPHICAL ABSTRACT\",\"PeriodicalId\":42612,\"journal\":{\"name\":\"Journal of Mathematics and the Arts\",\"volume\":\"18 1\",\"pages\":\"111 - 139\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-04-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematics and the Arts\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/17513472.2023.2199375\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics and the Arts","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/17513472.2023.2199375","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Sequence knitting comes from a straightforward directive; determine a short basic sequence of stitches and create a piece by continuous repetition of that sequence. This paper determines the number of sequence knitting patterns. We restrict our attention to sequences containing only knit and purl stitches and to flat knitting. We further assume that a sequence is restarted at the beginning of each row of knitting, but we do not assume that the number of stitches cast on is a multiple of the sequence length. We consider the case that a pattern and its left/right mirror image are the same, and the case that a pattern and its left/right mirror image are not necessarily the same. GRAPHICAL ABSTRACT