Applications of Quotient Posets [article]

Joshua Hallam
2014 arXiv   pre-print
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 lattices
more » ... ill also be shown to be a consequence of our factorization theorems. Finally we will use quotient posets to give unified proofs of some classic M\"obius function results.
arXiv:1411.3022v1 fatcat:rkcla744m5atzg7tsv552bjgpy