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We define a new family of overlaps $C_{N,m}$ for the XXZ Hamiltonian on aperiodic chain of length $N$. These are equal to the linear sums of thegroundstate components, in the canonical basis, wherein $m$ consecutive spinsare fixed to the state ${\uparrow}$. We define the boundary emptiness formationprobabilities as the ratios $C_{N,m}/C_{N,0}$ of these overlaps. In theassociated six-vertex model, they correspond to correlation functions on asemi-infinite cylinder of perimeter $N$. At the combinatorial point $\Delta =-\frac12$, we obtain closed-form expressions in terms of simple products ofratios of integers.

Boundary emptiness formation probabilities in the six-vertex model at $\Delta = -\frac12$