Factorization of the Characteristic PolynomialReport as inadecuate

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1 Department of Mathematics - University of Michigan

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.

Keywords : characterstic polynomial lattice Möbius function quotient supersolvability

Author: Joshua Hallam - Bruce Sagan -

Source: https://hal.archives-ouvertes.fr/


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