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In this paper we consider the characteristic polynomial of not necessarily ranked posets. We do so by allowing the rank to be an arbitrary function from the poset to the nonnegative integers. We will prove two results showing that the characteristic polynomial of a poset has nonnegative integral roots. Our factorization theorems will then be used to show that any interval of the Tamari lattice has a characteristic polynomial which factors in this way. Blass and Sagan's result about LL latticesarXiv:1411.3022v1 fatcat:rkcla744m5atzg7tsv552bjgpy