Every Poset Has a Central Element
نویسندگان
چکیده
It is proved that there exists a constant 6, f > 6 > 0, such that in every finite partially ordered set there is an element such that the fraction of order ideals containing that element is between 6 and 1 -6. It is shown that 6 can be taken to be at least (3-log, 5)/4~0.17. This settles a question asked independently by Colburn and Rival, and Rosenthal. The result implies that the information-theoretic lower bound for a certain class of search problems on partially ordered sets is tight up to a multiplicative constant. ( 1985 Academic Press. Inc.
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 40 شماره
صفحات -
تاریخ انتشار 1985