Chain polynomials of distributive lattices are 75 % unimodal
Abstract
It is shown that the numbers ci of chains of length i in the proper part L\0,1\ of a distributive lattice L of length +2 satisfy the inequalities c0<...<c /2 and c3 /4>...>c. This proves 75 % of the inequalities implied by the Neggers unimodality conjecture.
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