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New publication 'Latin hypercubes realizing integer partitions' by Diane Donovan, Tara Kemp, and James Lefevre. Abstract For an integer partition h1+⋯+hn=N, a 2-realization of this partition is a latin square of order N with disjoint subsquares of orders h1,…,hn. The existence of 2-realizations is a partially solved problem posed by Fuchs. In this paper, we extend Fuchs' problem to m-ary quasigroups, or, equivalently, latin hypercubes. We construct latin cubes for some partitions with at most two distinct parts and highlight how the new problem is related to the original. https://lnkd.in/gbdFxki8

Latin hypercubes realizing integer partitions

Latin hypercubes realizing integer partitions

arxiv.org

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