The Average Number of Linear Extensions of a Partial Order
نویسندگان
چکیده
Kleitman and Rothschild (Trans. Amer. Math. Soc. 205 (1975), 205-220) gave an asymptotic formula for the number of partial orders with ground-set In]. We give a shorter proof of their result and extend it to count the number of pairs (P, -<), where P is a partial order on [hi and -< is a linear extension of P. This gives us an asymptotic formula for (a) the average number of linear extensions of an n-element partial order and (b) the number of suborders of an n-element linear order. © 1996 Academic Press. Inc.
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 73 شماره
صفحات -
تاریخ انتشار 1996