Alternating planar algebra

The concept of alternating planar algebras first appeared in the work of Hernando Burgos-Soto on the Jones polynomial of alternating tangles. Alternating planar algebras provide an appropriate algebraic framework for other knot invariants in cases the elements involved in the computation are alternating. The concept has been used in extending to tangles some properties of Jones polynomial and Khovanov homology of alternating links.
Definition.
An alternating planar algebra is an oriented planar algebra, where the formula_1-input planar arc diagrams formula_2 satisfy the following conditions:
A planar arc diagram like this has been denominated type-formula_5 planar diagram.
Applications.
There are two known applications of the concept of alternating planar algebra.