Neural Codes and the Factor Complex

Abstract

We introduce the factor complex of a neural code, and show how intervals and maximal codewords are captured by the combinatorics of factor complexes. We use these results to obtain algebraic and combinatorial characterizations of max-intersection-complete codes, as well as a new combinatorial characterization of intersection-complete codes.

arXiv commentAdded a new section that takes computational considerations into account. That is, it compares an algorithm to determine max intersection completeness derived from our results with brute force methods