LACIM originated from a team of researchers in combinatorics created by Gilbert Labelle, Jacques Labelle, Pierre Leroux, François Bergeron and André Joyal, all Professors at Département de mathématiques (UQAM). The team wrote their first publications in the beginning of the 80’s and started about the same time the Séminaire de Combinatoire, which became the Séminaire du LACIM. In 1985, the combinatorics team was officially recognized as a research group by UQAM. In 1986, the first postdoctoral fellow Yeong-Nan Yeh was hired and the team was awarded with its first team grants from Québec (FCAC, who became FCAR then FRQNT). In 1990, the UQAM Centre institutionnel de recherche LACIM was created on these grounds.

Since its creation, the LACIM members supervised more than a hundred students (Master and PhD)  and  hosted more than 50 postdoctoral fellows who, for a large number of them, are today researchers in mathematics or computer science (these numbers are remarkable in Mathematics and Computer Science).

LACIM is one of the Centre de Recherches Mathématiques (CRM) laboratories.

Over the years, LACIM Directors were Pierre Leroux (1990-1994, 1999-2002 and 2005-2008), François Bergeron (1994-1998 and 2008-2014), Christophe Reutenauer (1998-1999 and 2002- 2005) and Srecko Brlek (2014-2016).