Bounded-degree coboundary expanders in every dimension at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Bounded-degree coboundary expanders in every dimension

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	counting, coloring	Levels:	1
Category:	Combinatorics	Lean version:	YES! ✔
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Bounded-degree coboundary expanders. Constructs arbitrarily large finite d-dimensional simplicial complexes, for every d ≥ 3, with uniformly bounded vertex degrees and uniform 𝔽₂ coboundary expansion in every degree below d. Together with the known graph and two-dimensional cases, this establishes the existence of such expanders in every positive dimension.

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LEVEL 1 Bounded-degree coboundary expanders in every dimension

released 2026-09-24 | 1 theorem · 4 lemmas · 9 proofs · 6,365 words | PLAY LEVEL 1 » (pdf)

For every integer d ≥ 3, we construct arbitrarily large finite d-dimensional simplicial complexes with uniformly bounded vertex degrees and uniform 𝔽₂ coboundary expansion in every degree below d. Together with the known graph and two-dimensional cases, this establishes the existence of bounded-degree 𝔽₂ coboundary expanders in every positive dimension.

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