Geometric Characterization of Hereditarily Bijective Boolean Networks

The study of relationships between structure and dynamics of asynchronous Boolean networks has recently led to the introduction of hereditarily bijective maps and even or odd self-dual networks. We show here that these two notions can be simply characterized geometrically: through orthogonality between certain affine subspaces. We also use this characterization to provide a construction of the class of hereditarily bijective maps, and to study its stability properties