# A note on maximally repeated sub-patterns of a point set

1 CASSIS - Combination of approaches to the security of infinite states systems
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174), Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We answer a question raised by P. Brass on the number of maximally repeated sub-patterns in a set of $n$ points in $\mathbbR^d$. We show that this number, which was conjectured to be polynomial, is in fact $\Theta(2^n/2)$ in the worst case, regardless of the dimension $d$.
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https://hal.inria.fr/inria-00070247
Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 7:39:18 PM
Last modification on : Friday, January 15, 2021 - 3:24:35 AM
Long-term archiving on: : Sunday, April 4, 2010 - 8:43:56 PM

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• HAL Id : inria-00070247, version 1

### Citation

Véronique Cortier, Xavier Goaoc, Mira Lee, Hyeon-Suk Na. A note on maximally repeated sub-patterns of a point set. [Research Report] RR-5773, INRIA. 2005, pp.5. ⟨inria-00070247⟩

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