We utilize the KOH theorem to prove the unimodality of integer partitions with at most a parts, all parts less than or equal to b, that are required to contain either repeated or consecutive parts. We connect this result to an open question in quantum physics relating the number of distinct total angular momentum multiplets of a system of N fermions, each with angular momentum ℓ, to those of a system in which each Fermion has angular momentum ℓ*=ℓ−N+1.