On an extremal problem for poset dimension
نویسندگان
چکیده
Let f(n) be the largest integer such that every poset on n elements has a 2-dimensional subposet on f(n) elements. What is the asymptotics of f(n)? It is easy to see that f(n) > n. We improve the best known upper bound and show f(n) = O(n). For higher dimensions, we show fd(n) = O ( n d d+1 ) , where fd(n) is the largest integer such that every poset on n elements has a d-dimensional subposet on fd(n) elements.
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عنوان ژورنال:
- CoRR
دوره abs/1705.00176 شماره
صفحات -
تاریخ انتشار 2017