Discrete Math Seminar: Bugs, colonies, and q-Boson normal ordering

In my work with Miguel Mendez, we provided a new combinatorial model for the coefficients appearing in the normal ordering of q-Boson words, by introducing combinatorial structures called bugs, colonies and settlements. In this lecture I will show, in a more general context, how this kind of structures can be used to simplify proofs of combinatorial theorems involving q-analogs, and how our combinatorial model and formulas for the coefficients appearing in the q-Boson normal ordering problem arise as a direct application of these techniques.