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Counterexamples to the Neggers-Stanley conjecture

Author: Petter Brändén
Journal: Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 155-158
MSC (2000): Primary 06A07, 26C10
Published electronically: December 24, 2004
MathSciNet review: 2119757
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Abstract | References | Similar Articles | Additional Information

Abstract: The Neggers-Stanley conjecture asserts that the polynomial counting the linear extensions of a labeled finite partially ordered set by the number of descents has real zeros only. We provide counterexamples to this conjecture.

References [Enhancements On Off] (What's this?)

  • 1. P. Brändén, Sign-graded posets, unimodality of $W$-polynomials and the Charney-Davis conjecture, Electr. J. Combin. 11(2), #9.
  • 2. Francesco Brenti, Unimodal, log-concave and Pólya frequency sequences in combinatorics, Mem. Amer. Math. Soc. 81 (1989), no. 413, viii+106. MR 963833, 10.1090/memo/0413
  • 3. L. H. Harper, Stirling behavior is asymptotically normal, Ann. Math. Statist. 38 (1967), 410–414. MR 0211432
  • 4. Joseph Neggers, Representations of finite partially ordered sets, J. Combin. Inform. System Sci. 3 (1978), no. 3, 113–133. MR 0551484
  • 5. Q. I. Rahman and G. Schmeisser, Analytic theory of polynomials, London Mathematical Society Monographs. New Series, vol. 26, The Clarendon Press, Oxford University Press, Oxford, 2002. MR 1954841
  • 6. V. Reiner and V. Welker, On the Charney-Davis and Neggers-Stanley conjectures, preprint; available at
  • 7. Rodica Simion, A multi-indexed Sturm sequence of polynomials and unimodality of certain combinatorial sequences, J. Combin. Theory Ser. A 36 (1984), no. 1, 15–22. MR 728500, 10.1016/0097-3165(84)90075-X
  • 8. Richard P. Stanley, Ordered structures and partitions, American Mathematical Society, Providence, R.I., 1972. Memoirs of the American Mathematical Society, No. 119. MR 0332509
  • 9. Richard P. Stanley, Hilbert functions of graded algebras, Advances in Math. 28 (1978), no. 1, 57–83. MR 0485835
  • 10. Richard P. Stanley, Combinatorics and commutative algebra, 2nd ed., Progress in Mathematics, vol. 41, Birkhäuser Boston, Inc., Boston, MA, 1996. MR 1453579
  • 11. David G. Wagner, Enumeration of functions from posets to chains, European J. Combin. 13 (1992), no. 4, 313–324. MR 1179527, 10.1016/S0195-6698(05)80036-8

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Additional Information

Petter Brändén
Affiliation: Department of Mathematics, Chalmers University of Technology and Göteborg University, S-412 96 Göteborg, Sweden

Keywords: Neggers-Stanley conjecture, partially ordered set, linear extension, real roots
Received by editor(s): August 31, 2004
Published electronically: December 24, 2004
Communicated by: Sergey Fomin
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.