ABSTRACTWe begin with a review of combinatorial hives as introduced by Knutson and Tao, and focus on a conjecture by Danilov and Koshevoy for generating hives from Hermitian matrix pairs. We examine a proposal by Appleby and Whitehead in the spirit of this conjecture and analytically elucidate an obstruction in their construction for guaranteeing hive generation, while detailing stronger conditions under which we can produce hives with almost certain probability. We provide the first mapping of this prescription onto a practical algorithmic space that enables affirming computational results and opens a new area of research into the analysis of the random geometries of hive surfaces.The second part of this article concerns methods of estimating Littlewood–Richardson coefficients from hives. We illustrate experimental confirmation and characterize two numerical algorithms: a rounded estimator on the continuous hive polytope following Narayanan, and a novel construction using a coordinate hit-and-run on the hive lattice.