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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Counterexamples to the poset conjectures of Neggers, Stanley, and Stembridge
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by John R. Stembridge PDF
Trans. Amer. Math. Soc. 359 (2007), 1115-1128 Request permission

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.
References
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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
  • Received by editor(s): December 6, 2004
  • Published electronically: July 21, 2006
  • Additional Notes: This work was supported by NSF grant DMS–0245385.
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2262844