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In this paper, a link between polymatroid theory and locally repairable codes (LRCs) is established. The codes considered here are completely general in that they are subsets of A^n, where A is an arbitrary finite set. Three classes of LRCs are considered, both with and without availability, and for both information-symbol and all-symbol locality. The parameters and classes of LRCs are generalized to polymatroids, and a general- ized Singelton bound on the parameters for these three classes ofarXiv:1510.02499v1 fatcat:qkkkameedvc3vka4ddjwfrawqi