Chain Polynomials of Distributive Lattices are 75% Unimodal
نویسندگان
چکیده
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 l + 2 satisfy the inequalities c0 < . . . < c⌊l/2⌋ and c⌊3l/4⌋ > . . . > cl. This proves 75 % of the inequalities implied by the Neggers unimodality conjecture.
منابع مشابه
Chain polynomials of distributive lattices
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 < . . . < cb`/2c and cb3`/4c > . . . > c`. This proves 75 % of the inequalities implied by the Neggers unimodality conjecture.
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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 l + 2 satisfy the inequalities c0 < . . . < c⌊l/2⌋ and c⌊3l/4⌋ > . . . > cl. This proves 75 % of the inequalities implied by the Neggers unimodality conjecture.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 12 شماره
صفحات -
تاریخ انتشار 2005