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Counterexamples to the Neggers-Stanley conjecture

Petter Brändén
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Abstract

The Neggers-Stanley conjecture (also known as the Poset conjecture) asserts that the polynomial counting the linear extensions of a partially ordered set on $\{1,2,...,p\}$ by their number of descents has real zeros only. We provide counterexamples to this conjecture.

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Petter Brändén. 2004-09-23. Counterexamples to the Neggers-Stanley conjecture. https://arxiv.org/abs/math/0408312

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