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Factorization of the Characteristic Polynomial

Abstract : We introduce a new method for showing that the roots of the characteristic polynomial of a finite lattice are all nonnegative integers. Our method gives two simple conditions under which the characteristic polynomial factors. We will see that Stanley's Supersolvability Theorem is a corollary of this result. We can also use this method to demonstrate a new result in graph theory and give new proofs of some classic results concerning the Möbius function.
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https://hal.inria.fr/hal-01207579
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Joshua Hallam, Bruce E. Sagan. Factorization of the Characteristic Polynomial. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.125-136, ⟨10.46298/dmtcs.2386⟩. ⟨hal-01207579⟩

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