This leads to a quest for the existence of extremely non-partitionable simplicial complexes.
Benjamin Nill, Kathrin Vorwerk 2008, 'Stanley's conjecture, cover depth and extremal simplicial complexes', Le Matematichehttp://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/75. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Interestingly, theta precession also increased the number of spurious loops during simplicial complex formation.
Mamiko Arai, Vicky Brandt, Yuri Dabaghian 2014, 'The effects of theta precession on spatial learning and simplicial complex dynamicsin a topological model of the hippocampal spatial map.', PLoS Computational Biologyhttp://europepmc.org/articles/PMC4063672?pdf=render. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We compare our results to a naive simplicial complexes reconstruction based on edge length.
S. Guinard, B. Vallet 2018, 'SENSOR-TOPOLOGY BASED SIMPLICIAL COMPLEX RECONSTRUCTION FROM MOBILE LASER SCANNING',ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Scienceshttps://www.isprs-ann-photogramm-remote-sens-spatial-inf-sci.net/IV-2/121/2018/isprs-annals-IV-2-121-2018.pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The intersection matrix of a simplicial complex has entries equal to the rank of the intersecction of its facets.
Arocha Jorge L., Bracho Javier, García-Colín Natalia, Hubard Isabel 2015, 'Reconstructing Surface Triangulations by Their Intersection Matrices 26 September2014', Discussiones Mathematicae Graph Theoryhttp://www.degruyter.com/view/j/dmgt.2015.35.issue-3/dmgt.1816/dmgt.1816.xml?format=INT. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
A new characterization of unichord-free graphs corresponds to a suitable reformulation of the standard simplicial vertex characterization of chordal graphs.
McKee Terry A. 2015, 'A New Characterization of Unichord-Free Graphs', Discussiones Mathematicae Graph Theoryhttp://www.degruyter.com/view/j/dmgt.2015.35.issue-4/dmgt.1831/dmgt.1831.xml?format=INT. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)