{"title":"0021-避免反转序列树的生成及Hong和Li的猜想","authors":"T. Mansour","doi":"10.47443/dml.2023.012","DOIUrl":null,"url":null,"abstract":"An inversion sequence of length n is a word e = e 0 · · · e n which satisfies, for each i ∈ [ n ] = { 0 , 1 , . . . , n } , the inequality 0 ≤ e i ≤ i . In this paper, by generating tree tools, an explicit formula is found for the generating function for the number of inversion sequences of length n that avoid 0021 , which resolves the conjecture of Hong and Li posed in the recent paper [ Electron. J. Combin. 29 (2022) #4.37].","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Generating Trees for 0021-Avoiding Inversion Sequences and a Conjecture of Hong and Li\",\"authors\":\"T. Mansour\",\"doi\":\"10.47443/dml.2023.012\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An inversion sequence of length n is a word e = e 0 · · · e n which satisfies, for each i ∈ [ n ] = { 0 , 1 , . . . , n } , the inequality 0 ≤ e i ≤ i . In this paper, by generating tree tools, an explicit formula is found for the generating function for the number of inversion sequences of length n that avoid 0021 , which resolves the conjecture of Hong and Li posed in the recent paper [ Electron. J. Combin. 29 (2022) #4.37].\",\"PeriodicalId\":36023,\"journal\":{\"name\":\"Discrete Mathematics Letters\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-03-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics Letters\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.47443/dml.2023.012\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47443/dml.2023.012","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Generating Trees for 0021-Avoiding Inversion Sequences and a Conjecture of Hong and Li
An inversion sequence of length n is a word e = e 0 · · · e n which satisfies, for each i ∈ [ n ] = { 0 , 1 , . . . , n } , the inequality 0 ≤ e i ≤ i . In this paper, by generating tree tools, an explicit formula is found for the generating function for the number of inversion sequences of length n that avoid 0021 , which resolves the conjecture of Hong and Li posed in the recent paper [ Electron. J. Combin. 29 (2022) #4.37].