Dumont-Thomas整数数制的位置性
Positionality of Dumont--Thomas numeration systems for integers
AI总结：
本文研究Dumont-Thomas数制的位置性条件，通过分析生成替换的性质，推导出其数制是否满足位置性的判定方法，并与已有文献中的相关性质建立联系。
摘要：
本文研究Dumont-Thomas数制的位置性条件，通过分析生成替换的性质，推导出其数制是否满足位置性的判定方法，并与已有文献中的相关性质建立联系。
英文摘要：
Introduced in 2001 by Lecomte and Rigo, abstract numeration systems provide a way of expressing natural numbers with words from a language $L$ accepted by a finite automaton. As it turns out, these numeration systems are not necessarily positional, i.e., we cannot always find a sequence $U=(U_i)_{i\ge 0}$ of integers such that the value of every word in the language $L$ is determined by the position of its letters and the first few values of $U$. Finding the conditions under which an abstract numeration system is positional seems difficult in general. In this paper, we thus consider this question for a particular sub-family of abstract numeration systems called Dumont--Thomas numeration systems. They are derived from substitutions and were introduced in 1989 by Dumont and Thomas. We exhibit conditions on the underlying substitution so that the corresponding Dumont--Thomas numeration is positional. We first work in the most general setting, then particularize our results to some practical cases. Finally, we link our numeration systems to existing literature, notably properties studied by Rényi in 1957, Parry in 1960, Bertrand-Mathis in 1989, and Fabre in 1995
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
