solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看3027次
Formal inverses of the generalized Thue-Morse sequences and variations of the Rudin-Shapiro sequence. (arXiv:1810.03533v1 [math.NT])
来源于:arXiv
A formal inverse of a given automatic sequence (the sequence of coefficients
of the composition inverse of its associated formal power series) is also
automatic. The comparison of properties of the original sequence and its formal
inverse is an interesting problem. Such an analysis has been done before for
the Thue{Morse sequence. In this paper, we describe arithmetic properties of
formal inverses of the generalized Thue-Morse sequences and formal inverses of
two modifications of the Rudin{Shapiro sequence. In each case, we give the
recurrence relations and the automaton, then we analyze the lengths of strings
of consecutive identical letters as well as the frequencies of letters. We also
compare the obtained results with the original sequences. 查看全文>>