Forbidden Subposets in the Cycle Poset

چکیده مقاله

The cycle poset consists of the intervals of the cyclic permutation of the elements 1, 2, …, n, ordered by inclusion. Suppose that F is a set of such intervals, none of them is a less than s others. The maximum size of F is determined under this condition. It is also shown that if the largest size of a set in this poset without containing a small subposet P is known, it solves the same problem, up to an additive constant, in the grid poset consisting of the pairs (i, j)(1 ≤ i, j ≤ n) and ordered coordinate-wise.