Order-forcing in Neural Codes
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454_2025_Article_760.pdf
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4.68 MB
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Adobe PDF
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58c1748e067fe65a6beb3e0446810dd0
Author(s)
Jeffs, R. A.
Lienkaemper, Caitlin
Youngs, Nora
Date Issued
October 28, 2025
Journal
Discrete & Computational Geometry
Publisher
Springer US
Citation
Jeffs, R.A., Lienkaemper, C. & Youngs, N. Order-forcing in Neural Codes. Discrete Comput Geom (2025).
Version
Final published version
Abstract
Convex neural codes are subsets of the Boolean lattice that record the intersection patterns of convex sets in Euclidean space. Much work in recent years has focused on finding combinatorial criteria on codes that can be used to classify whether or not a code is convex. In this paper we introduce order-forcing, a combinatorial tool which recognizes when certain regions in a realization of a code must appear along a line segment between other regions. We use order-forcing to construct novel examples of non-convex codes, and to expand existing families of examples. We also construct a family of codes which shows that a dimension bound of Cruz, Giusti, Itskov, and Kronholm (referred to as monotonicity of open convexity) is tight in all dimensions.
MIT Department
Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00454-025-00760-3
