Fence (mathematics)

In mathematics, a fence, also called a zigzag poset, is a partially ordered set (poset) in which the order relations form a path with alternating orientations: or A fence may be finite, or it may be formed by an infinite alternating sequence extending in both directions.

The incidence posets of path graphs form examples of fences.

A linear extension of a fence is called an alternating permutation; André's problem of counting the number of different linear extensions has been studied since the 19th century.

[2] A partially ordered set is series-parallel if and only if it does not have four elements forming a fence.

[5] For instance, Q(2,9) has the elements and relations In this notation, a fence is a partially ordered set of the form Q(1,n).