Cardinal invariants associated with the combinatorics of the uniformity number of the ideal of meager-additive sets

In [CMRM24], it was proved that it is relatively consistent that \emph{bounding number} $\mathfrak{b}$ is smaller than the uniformity of $\mathcal{M}\mathcal{A}$, where $\mathcal{M}\mathcal{A}$ denotes the ideal of the meager-additive sets of $2^{\omega }$. To establish this result, a specific cardinal invariant, which we refer to as ${\mathfrak{b}}_b^{\mathsf{e}\mathsf{q}}$, was introduced in close relation to Bartoszyński’s and Judah’s characterization of the uniformity of $\mathcal{M}\mathcal{A}$. This survey aims to explore this cardinal invariant along with its dual, which we call as ${\mathfrak{d}}_b^{\mathsf{e}\mathsf{q}}$. In particular, we will illustrate its connections with the cardinals represented in Cichoń’s diagram. Furthermore, we will present several open problems pertaining to these cardinals.