Fence

A fence is a structure that encloses an area, typically outdoors, and is usually constructed from posts that are connected by boards, wire, rails or netting. A fence differs from a wall in not having a solid foundation along its whole length.

Alternatives to fencing include a ditch (sometimes filled with water, forming a moat).

Types

By function

Fence (mathematics)

In mathematics, a fence, also called a zigzag poset, is a partially ordered set 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. The solutions to this counting problem, the so-called Euler zigzag numbers or up/down numbers, are

The number of antichains in a fence is a Fibonacci number; the distributive lattice with this many elements, generated from a fence via Birkhoff's representation theorem, has as its graph the Fibonacci cube.

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

Several authors have also investigated the number of order-preserving maps from fences to themselves, or to fences of other sizes.

Horse jumping obstacles

Various obstacles are found in competitive sports involving horse jumping. These include show jumping, hunter, and the cross-country phase of the equestrian discipline of eventing. The size and type of obstacles vary depending on the course and the level of the horse and rider, but all horses must successfully negotiate these obstacles in order to complete a competition. Fences used in hunter and eventing are generally made to look relatively rustic and natural.

In jumping competition, they are often brightly colored and creatively designed. In hunter and jumper competition, obstacles are constructed to fall down if struck by the horse. In eventing, they are built to be solid, though for safety, certain elements may be designed to break away if hit.

Arrowhead

Also called chevrons, these fences are shaped like triangles, with the point facing towards the ground. They are generally very narrow, usually only a few feet wide. Arrowhead fences require the rider to keep their horse straight between their hands and legs, as it is easy for a run-out to occur due to the narrowness of the fence. These fences are often used in combination with other obstacles to increase their difficulty, such as right after a bank or as the second obstacle in a bending line. This tests the rider's ability to regain control of his/her horse following an obstacle.