On the number of neighborly simplices in \(\mathbb{R}^d\)

DOI10.1007/S00026-024-00694-2MaRDI QIDQ6621949

Andrzej Kisielewicz

Publication date: 21 October 2024

Published in: Annals of Combinatorics (Search for Journal in Brave)

zbMATH Keywords

boxcodeneighborly simplices

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Theory of error-correcting codes and error-detecting codes (94Bxx)

Cites Work

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• Polyboxes, cube tilings and rigidity
• Neighborly families of \(2^ k\) k-simplices in \(E^ k\).
• Mutually disjoint families of 0-1 sequences
• No more than \(2^{d+1}-2\) nearly neighbourly simplices in \({\mathbb{R}}^d\)
• No nine neighborly tetrahedra exist
• A Conjecture Concerning Neighboring Tetrahedra
• Proofs from THE BOOK
• New bounds on the maximum number of neighborly boxes in \(\mathbb{R}^d\)
• Exact values and improved bounds on \(k\)-neighborly families of boxes

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