  Let $0<k\in\mathbb{Z}$. We zipper-merge integer compositions with sums $k$
and $k+1$, equal number of parts and initial entries equal at least to 1 and 2,
respectively. This yields bitstrings with two initial zeros, $k-1$ remaining
zeros and $k$ ones. Tensors whose entries are such bitstrings contain unique
representations of all Dyck words of length $2k$. If rows and columns of such
tensors are disposed in descending lexicographic order, then their entries not
representing Dyck words form disjoint unions of descending staircases
corresponding to strict lower triangular submatrices.

Combinatorics