  We study the realizability of simplicial complexes with a given pair of
integer sequences, representing the node degree distribution and the facet size
distribution, respectively. While the $s$-uniform variant of the problem is
$\mathsf{NP}$-complete when $s \geq 3$, we identify two populations of input
sequences, most of which can be solved in polynomial time using a recursive
algorithm that we contribute. Combining with a sampler for the simplicial
configuration model [J.-G. Young $\textit{et al.}$, Phys. Rev. E $\textbf{96}$,
032312 (2017)], we facilitate the efficient sampling of simplicial ensembles
from arbitrary degree and size distributions. We find that, contrary to
expectations based on dyadic networks, increasing the nodes' degrees reduces
the number of loops in simplicial complexes. Our work unveils a fundamental
constraint on the degree-size sequences and sheds light on further analysis of
higher-order phenomena based on local structures.
