{"title":"排列中长度为5的模式的双射","authors":"Joanna N. Chen , Zhicong Lin","doi":"10.1016/j.jcta.2023.105815","DOIUrl":null,"url":null,"abstract":"<div><p><span><span>A bijection<span> which preserves five classical set-valued permutation </span></span>statistics between </span><span><math><mo>(</mo><mn>31245</mn><mo>,</mo><mn>32145</mn><mo>,</mo><mn>31254</mn><mo>,</mo><mn>32154</mn><mo>)</mo></math></span>-avoiding permutations and <span><math><mo>(</mo><mn>31425</mn><mo>,</mo><mn>32415</mn><mo>,</mo><mn>31524</mn><mo>,</mo><mn>32514</mn><mo>)</mo></math></span>-avoiding permutations is constructed. Combining this bijection with two codings of permutations introduced respectively by Baril–Vajnovszki and Martinez–Savage, we prove an enumerative conjecture posed by Gao and Kitaev. Moreover, the generating function for the common counting sequence is proved to be algebraic.</p></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A bijection for length-5 patterns in permutations\",\"authors\":\"Joanna N. Chen , Zhicong Lin\",\"doi\":\"10.1016/j.jcta.2023.105815\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span><span>A bijection<span> which preserves five classical set-valued permutation </span></span>statistics between </span><span><math><mo>(</mo><mn>31245</mn><mo>,</mo><mn>32145</mn><mo>,</mo><mn>31254</mn><mo>,</mo><mn>32154</mn><mo>)</mo></math></span>-avoiding permutations and <span><math><mo>(</mo><mn>31425</mn><mo>,</mo><mn>32415</mn><mo>,</mo><mn>31524</mn><mo>,</mo><mn>32514</mn><mo>)</mo></math></span>-avoiding permutations is constructed. Combining this bijection with two codings of permutations introduced respectively by Baril–Vajnovszki and Martinez–Savage, we prove an enumerative conjecture posed by Gao and Kitaev. Moreover, the generating function for the common counting sequence is proved to be algebraic.</p></div>\",\"PeriodicalId\":50230,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series A\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory Series A\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0097316523000833\",\"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/S0097316523000833","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A bijection which preserves five classical set-valued permutation statistics between -avoiding permutations and -avoiding permutations is constructed. Combining this bijection with two codings of permutations introduced respectively by Baril–Vajnovszki and Martinez–Savage, we prove an enumerative conjecture posed by Gao and Kitaev. Moreover, the generating function for the common counting sequence is proved to be algebraic.
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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