Factorization of the Characteristic Polynomial

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...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science 2014-01, Vol.DMTCS Proceedings vol. AT,... (Proceedings), p.125-136
Main Authors: Hallam, Joshua, Sagan, Bruce
Format: Article
Language:English
Subjects:
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[math.math-co] mathematics [math]/combinatorics [math.co]
characterstic polynomial
Combinatorics
Computer Science
Discrete Mathematics
lattice
Mathematics
möbius function
quotient
supersolvability
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Summary: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.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.2386