Abstract: We consider a particular type of linear numeration systems called confluent systems. These systems are generated from a linear recurrence with restricted coefficients. We associate a so-called Erd\H{o} measure to this system. In a general setting, it remains an open problem to completely classify which of these measures are purely singular and which are absolutely continuous with respect to Lebesgue measure. In this talk, we discuss the Garsia entropy of such systems and the issues associated with a word combinatorial approach to more general systems, along with open problems.