{"title":"长度为 4 的图案的 Wilf 等价性的进一步完善","authors":"Robin D.P. Zhou , Yongchun Zang , Sherry H.F. Yan","doi":"10.1016/j.jcta.2024.105863","DOIUrl":null,"url":null,"abstract":"<div><p><span><span>In this paper, we construct a bijection<span> between 3142-avoiding permutations and 3241-avoiding permutations which proves the </span></span>equidistribution of five classical set-valued </span>statistics. Our bijection also enables us to establish a bijection between 3142-avoiding permutations and 4132-avoiding permutations, and a bijection between 2413-avoiding permutations and 1423-avoiding permutations, both of which preserve five classical set-valued statistics. Our results are generalizations of several conjectures posed by Burstein.</p></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"204 ","pages":"Article 105863"},"PeriodicalIF":0.9000,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Further refinements of Wilf-equivalence for patterns of length 4\",\"authors\":\"Robin D.P. Zhou , Yongchun Zang , Sherry H.F. Yan\",\"doi\":\"10.1016/j.jcta.2024.105863\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span><span>In this paper, we construct a bijection<span> between 3142-avoiding permutations and 3241-avoiding permutations which proves the </span></span>equidistribution of five classical set-valued </span>statistics. Our bijection also enables us to establish a bijection between 3142-avoiding permutations and 4132-avoiding permutations, and a bijection between 2413-avoiding permutations and 1423-avoiding permutations, both of which preserve five classical set-valued statistics. Our results are generalizations of several conjectures posed by Burstein.</p></div>\",\"PeriodicalId\":50230,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series A\",\"volume\":\"204 \",\"pages\":\"Article 105863\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-01-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory Series A\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0097316524000025\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series A","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0097316524000025","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Further refinements of Wilf-equivalence for patterns of length 4
In this paper, we construct a bijection between 3142-avoiding permutations and 3241-avoiding permutations which proves the equidistribution of five classical set-valued statistics. Our bijection also enables us to establish a bijection between 3142-avoiding permutations and 4132-avoiding permutations, and a bijection between 2413-avoiding permutations and 1423-avoiding permutations, both of which preserve five classical set-valued statistics. Our results are generalizations of several conjectures posed by Burstein.
期刊介绍：
The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.
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