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## Counterexamples to the Neggers-Stanley conjecture

### Petter Brändén

**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.

*Copyright 2004 American Mathematical Society
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#### Article Info

- ERA Amer. Math. Soc.
**10** (2004), pp. 155-158
- Publisher Identifier: S 1079-6762(04)00140-4
- 2000
*Mathematics Subject Classification*. Primary 06A07, 26C10
*Key words and phrases.* Neggers-Stanley conjecture, partially ordered set, linear extension, real roots
- Received by editors August 31, 2004
- Posted on December 24, 2004
- Communicated by Sergey Fomin
- Comments (When Available)

**Petter Brändén**

Department of Mathematics, Chalmers University of Technology and Göteborg University, S-412~96 Göteborg, Sweden

*E-mail address:* `branden@math.chalmers.se`

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