McMullen--Walkup generalized lower bound conjecture

Let $\Delta$ be the boundary of a simplicial convex $d$-polytope. For $1\leq r\leq\lfloor d/2\rfloor$, let $g_r(\Delta)$ denote the $r$th entry of its $g$-vector, and call $\Delta$ $(r-1)$-stacked when it is the boundary of an $(r-1)$-stacked homology ball. McMullen--Walkup generalized lower bound conjecture. For every $1\leq r\leq\lfloor d/2\rfloor$, one has $g_r(\Delta)\geq 0$, with equality if and only if $\Delta$ is $(r-1)$-stacked. The nonnegativity is part of the generalized lower bound theorem for simplicial polytopes, while the equality characterization is the conjectural aspect; the source presents this as the generalized lower bound conjecture.