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The hive model is a combinatorial device that may be used to determineLittlewood-Richardson coefficients and study their properties. It represents analternative to the use of the Littlewood-Richardson rule. Here properties ofhives are used to determine all possible multiplicity-free Schur functionproducts and skew Schur function expansions. This confirms the results ofStembridge, Gutschwager, and Thomas and Yong, and sheds light on thecombinatorial origin of the conditions for being multiplicity-free, as well asillustrating some of the key features and power of the hive model.

A hive model determination of multiplicity-free Schur function products and skew Schur functions