Geodesic
Chain polynomials of distributive lattices are 75\% unimodal
The electronic journal of combinatorics, Tome 12 (2005)

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Zbl arXiv EuDML
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.
DOI : 10.37236/1971
Classification : 05E99, 06A07
Mots-clés : finite poset, unimodality, Neggers-Stanley conjecture 
Anders Björner; Jonathan David Farley. Chain polynomials of distributive lattices are 75\% unimodal. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1971
@article{10_37236_1971,
     author = {Anders Bj\"orner and Jonathan David Farley},
     title = {Chain polynomials of distributive lattices are 75\% unimodal},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1971},
     zbl = {1064.05154},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1971/}
}
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