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On the number of pairwise touching simplices

Lemmens, Bas, Parsons, Christopher (2015) On the number of pairwise touching simplices. Involve: A Journal of Mathematics, 8 (3). pp. 513-520. ISSN 1944-4176. E-ISSN 1944-4184. (doi:10.2140/involve.2015.8.513) (KAR id:43592)

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http://dx.doi.org/10.2140/involve.2015.8.513

Abstract

In this note, it is shown that the maximum number of pairwise touching translates of an n -simplex is at least n+3 for n=7 , and for all n?5 such that n?1mod4 . The current best known lower bound for general n is n+2 . For n=2 k ?1 and k?2 , we will also present an alternative construction to give n+2 touching simplices using Hadamard matrices.

Item Type: Article
DOI/Identification number: 10.2140/involve.2015.8.513
Subjects: Q Science
Q Science > QA Mathematics (inc Computing science) > QA165 Combinatorics
Q Science > QA Mathematics (inc Computing science) > QA440 Geometry
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Bas Lemmens
Date Deposited: 22 Oct 2014 11:43 UTC
Last Modified: 06 Feb 2020 04:10 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/43592 (The current URI for this page, for reference purposes)
Lemmens, Bas: https://orcid.org/0000-0001-6713-7683
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