THE TEACHING OF MATHEMATICS

THE TEACHING OF MATHEMATICS
A brief introduction to hypergraph expanders and the coboundary expansion of $\Lambda_n^3$
Ilija Vrećica

Abstract

Building on the ideas from [P. F. Wild, High-dimensional expansion and crossing numbers of simplicial complexes, Doctoral thesis submitted to Graduate School of the Institute of Science and Technology Austria, 2022], in this paper we obtain an upper bound for the expansion coefficient (Cheeger constant) $\eta_1(\Lambda_n^3)$ of the complete, multipartite complex $\Lambda_n^3$. We take this particular calculation as an opportunity to give the reader a glimpse into the general theory of graph expanders and their higher dimensional analogues.

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Keywords: Expander graphs; high dimensional expanders; cohomology.

DOI: 10.57016/TM-TXJC3699

Pages:  42$-$56     

Volume  XXIX ,  Issue  1 ,  2026