{"title":"避免使用 021 和另一个长度为 4 的图案的反转序列","authors":"Toufik Mansour, Gökhan Yıldırım","doi":"10.46298/dmtcs.10444","DOIUrl":null,"url":null,"abstract":"We study the enumeration of inversion sequences that avoid the pattern 021 and another pattern of length four. We determine the generating trees for all possible pattern pairs and compute the corresponding generating functions. We introduce the concept of dregular generating trees and conjecture that for any 021-avoiding pattern τ , the generating tree T ({021, τ }) is d-regular for some integer d.","PeriodicalId":412397,"journal":{"name":"Discrete Mathematics & Theoretical Computer Science","volume":"33 6","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inversion sequences avoiding 021 and another pattern of length four\",\"authors\":\"Toufik Mansour, Gökhan Yıldırım\",\"doi\":\"10.46298/dmtcs.10444\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the enumeration of inversion sequences that avoid the pattern 021 and another pattern of length four. We determine the generating trees for all possible pattern pairs and compute the corresponding generating functions. We introduce the concept of dregular generating trees and conjecture that for any 021-avoiding pattern τ , the generating tree T ({021, τ }) is d-regular for some integer d.\",\"PeriodicalId\":412397,\"journal\":{\"name\":\"Discrete Mathematics & Theoretical Computer Science\",\"volume\":\"33 6\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics & Theoretical Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/dmtcs.10444\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics & Theoretical Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/dmtcs.10444","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
我们研究了避免 021 图案和另一个长度为 4 的图案的反转序列的枚举。我们确定了所有可能模式对的生成树，并计算了相应的生成函数。我们引入了不规则生成树的概念，并猜想对于任何避开 021 图案 τ 的生成树 T ({021, τ }) 对于某个整数 d 是不规则的。
Inversion sequences avoiding 021 and another pattern of length four
We study the enumeration of inversion sequences that avoid the pattern 021 and another pattern of length four. We determine the generating trees for all possible pattern pairs and compute the corresponding generating functions. We introduce the concept of dregular generating trees and conjecture that for any 021-avoiding pattern τ , the generating tree T ({021, τ }) is d-regular for some integer d.
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