Eye of a Chain

An eye of a chain is a term which can be used to render Benson's definition of unconditional life. In that article such an eye is also called a “black-enclosed region vital to a black chain in a group” (if the group is black).

Patrick Traill: 2018-09-09: I think that the article currently omits ‘in a group’.

Benson's definition specifies that a group consisting of a collection of chains is unconditionally alive if each of those chains has two ‘eyes’ ‘enclosed’ in the group; such an eye E of a chain C is a maximal strictly connected set of empty points and opposing stones ‘enclosed’ by the group in which every empty point is adjacent to C (is a liberty of C). If suicide is allowed, then any opposing stones in E must also all be adjacent to C.

Benson's Theorem says that unconditional life is equivalent to being pass-alive.

When the group is a single chain, this is equivalent to the conventional idea of an eye of a group.

See also

• Benson's definition of unconditional life.
• Formal definitions of eye has a summary of Benson's Theorem and his definition.