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{\bf Anders Bj\"orner and Jonathan David Farley}
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{\bf Chain Polynomials of Distributive Lattices are 75\% Unimodal}
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It is shown that the numbers $c_i$ of chains of length $i$
in the proper part $L\setminus\{0,1\}$ of a distributive 
lattice $L$ of length $\ell +2$ satisfy the inequalities
$$c_0<\ldots<c_{\lfloor{\ell /2}\rfloor} \quad\hbox{ and }\quad
c_{\lfloor{3 \ell /4}\rfloor}>\ldots>c_{\ell}.$$
This proves 75\% of the inequalities implied by the 
Neggers unimodality conjecture.

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