bibkey: dotterrer2012coboundary authors: Dominic Dotterrer, Matthew Kahle year: 2012 title: “Coboundary expanders” doi: 10.1142/S1793525312500197 url: https://arxiv.org/abs/1012.5316v2 claim: “Proposition 5.5 gives the cross-polytope coboundary expansion lower bound 2(n-k-1)/(k+2), hence 2R <= 3T for n=3 and k=1 in support-count norms.” strata_touched:

• D5/S3/Combinatorics/Graph/TripartiteH1Repair license: citation-only triage: anchor

Cross-polytope coboundary expansion

Verified locator

DOI: 10.1142/S1793525312500197

URL: https://arxiv.org/abs/1012.5316v2

• Locator: Section 2 defines the cochain norm by support size.
• Locator: Proposition 5.5 gives the cross-polytope boundary expansion bound $2(n-k-1)/(k+2)$; at $n=3$, $k=1$ this is $T/R\ge 2/3$.

Dotterrer and Kahle, Coboundary expanders, Proposition 5.5, proves a coboundary expansion estimate for the cross-polytope boundary. Their Section 2 defines the cochain norm as support size. At three opposite vertex pairs and degree one, its bound is $T/R\ge 2/3$, equivalently $2R\le 3T$ for raw edge and triangle counts. Dividing each count by the number of edges or triangles would give a different normalized ratio. The proposition supplies the published upper bound. The three-edge antipodal equality witness in the repository is a separate, directly formalized construction.