[en] 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 R\'{e}nyi in 1957, Parry in 1960,
Bertrand-Mathis in 1989, and Fabre in 1995.
