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Counterexamples to the poset conjectures of Neggers, Stanley, and Stembridge


Author: John R. Stembridge
Journal: Trans. Amer. Math. Soc. 359 (2007), 1115-1128
MSC (2000): Primary 06A07, 06-04, 05A15
DOI: https://doi.org/10.1090/S0002-9947-06-04271-1
Published electronically: July 21, 2006
MathSciNet review: 2262844
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Abstract: We provide the first counterexamples to Neggers' 1978 conjecture and Stembridge's 1997 conjecture that the generating functions for descents and peaks in the linear extensions of naturally labeled posets should have all real zeros. We also provide minimum-sized counterexamples to a generalization of the Neggers conjecture due to Stanley that was recently disproved by Brändén.


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Additional Information

John R. Stembridge
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109–1109
Email: jrs@umich.edu

DOI: https://doi.org/10.1090/S0002-9947-06-04271-1
Received by editor(s): December 6, 2004
Published electronically: July 21, 2006
Additional Notes: This work was supported by NSF grant DMS–0245385.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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