Counting Partial Orders With A Fixed Number Of Comparable Pairs
نویسندگان
چکیده
In 1978, Dhar suggested a model of a lattice gas whose states are partial orders. In this context he raised the question of determining the number of partial orders with a xed number of comparable pairs. Dhar conjectured that in order to nd a good approximation to this number, it should suuce to enumerate families of layer posets. In this paper we prove this conjecture and thereby prepare the ground for a complete answer to the question.
منابع مشابه
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عنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 10 شماره
صفحات -
تاریخ انتشار 2001