Regressions and monotone chains: a ramsey - type extermal problem for partial orders
نویسندگان
چکیده
A regression is a function g from a partially ordered set to itself such that g(x)~_x for all z. A monotone k-chain is a chain of k elements xx<x2< . . . . .xk such that g(xO~g(x~)~_...~_g(xk). If a partial order has sufficiently many elements compared to the size of its largest antichain, every regression on it will have a monotone (k+ l)-chain. Fixing w, let f(w, k) be the smallest number such that every regression on every partial order with size least f(w, k) but no antichain larger than w has a monotone (k-'-1)-chain. We show that f(w, k)=(w+ 1) k.
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ورودعنوان ژورنال:
- Combinatorica
دوره 4 شماره
صفحات -
تاریخ انتشار 1984