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

翻译：摘要：Lecomte与Rigo于2001年提出的抽象进位系统，提供了一种利用有限自动机所接受的语言$L$中的单词表达自然数的方法。研究表明，此类进位系统未必具有位置性，即我们无法总是找到整数序列$U=(U_i)_{i\ge 0}$，使得语言$L$中每个单词的值由字母的位置及$U$的前若干项唯一确定。寻找抽象进位系统具有位置性的条件在一般情况下颇具难度。因此，本文针对抽象进位系统的一个特定子类——Dumont–Thomas进位系统——探讨该问题。这类系统源于字母替换，由Dumont与Thomas于1989年提出。我们揭示了底层替换需满足的条件，使得相应的Dumont–Thomas进位系统具有位置性。首先在最具普适性的框架下开展工作，随后将结果具体化至若干实际情形。最后，将本进位系统与现有文献建立关联，尤其涉及Rényi（1957年）、Parry（1960年）、Bertrand-Mathis（1989年）及Fabre（1995年）所研究的性质。