{"title":"Apwenian数列的计算机辅助证明","authors":"Hao Fu, Guo-Niu Han","doi":"10.1145/2930889.2930891","DOIUrl":null,"url":null,"abstract":"An infinite ±1-sequence is called Apwenian if its Hankel determinant of order n divided by 2n-1 is an odd number for every positive integer n. In 1998, Allouche, Peyriere, Wen and Wen discovered and proved that the Thue--Morse sequence is an Apwenian sequence by direct determinant manipulations. Recently, Bugeaud and Han re-proved the latter result by means of an appropriate combinatorial method. By significantly improving the combinatorial method, we find several new Apwenian sequences with Computer Assistance. This research has application in Number Theory to determining the irrationality exponents of some transcendental numbers.","PeriodicalId":169557,"journal":{"name":"Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation","volume":"110 8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Computer Assisted Proof for Apwenian Sequences\",\"authors\":\"Hao Fu, Guo-Niu Han\",\"doi\":\"10.1145/2930889.2930891\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An infinite ±1-sequence is called Apwenian if its Hankel determinant of order n divided by 2n-1 is an odd number for every positive integer n. In 1998, Allouche, Peyriere, Wen and Wen discovered and proved that the Thue--Morse sequence is an Apwenian sequence by direct determinant manipulations. Recently, Bugeaud and Han re-proved the latter result by means of an appropriate combinatorial method. By significantly improving the combinatorial method, we find several new Apwenian sequences with Computer Assistance. This research has application in Number Theory to determining the irrationality exponents of some transcendental numbers.\",\"PeriodicalId\":169557,\"journal\":{\"name\":\"Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation\",\"volume\":\"110 8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-07-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2930889.2930891\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2930889.2930891","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An infinite ±1-sequence is called Apwenian if its Hankel determinant of order n divided by 2n-1 is an odd number for every positive integer n. In 1998, Allouche, Peyriere, Wen and Wen discovered and proved that the Thue--Morse sequence is an Apwenian sequence by direct determinant manipulations. Recently, Bugeaud and Han re-proved the latter result by means of an appropriate combinatorial method. By significantly improving the combinatorial method, we find several new Apwenian sequences with Computer Assistance. This research has application in Number Theory to determining the irrationality exponents of some transcendental numbers.
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