GAPS IN THE THUE-MORSE WORD

被引：0
|
作者：
Spiegelhofer, Lukas [1 ]
机构：
[1] Univ Leoben, Math, Leoben, Austria
来源：
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2023年 / 114卷 / 01期
基金：
奥地利科学基金会;
关键词：
Thue-Morse sequence; subword occurrence; morphic sequence; k-kernel; SEQUENCES; SQUARES; RING;
D O I：
10.1017/S1446788721000380
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Thue-Morse sequence is a prototypical automatic sequence found in diverse areas of mathematics, and in computer science. We study occurrences of factors w within this sequence, or more precisely, the sequence of gaps between consecutive occurrences. This gap sequence is morphic; we prove that it is not automatic as soon as the length of w is at least 2, thereby answering a question by J. Shallit in the affirmative. We give an explicit method to compute the discrepancy of the number of occurrences of the block (empty set)1 in the Thue-Morse sequence. We prove that the sequence of discrepancies is the sequence of output sums of a certain base-2 transducer.
引用
收藏
页码：110 / 144
页数：35
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