The Joints Problem in $\mathbb{R}^n

The Joints Problem in $\mathbb{R}^n

We show that given a collection of $A$ lines in $\mathbb{R}^n$, $n\geq2$, the maximum number of their joints (points incident to at least $n$ lines whose directions form a linearly independent set) is $O(A^{n/(n-1)})$. An analogous result for smooth algebraic curves is also proven.

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Veröffentlicht in:SIAM journal on discrete mathematics 2010-10, Vol.23 (4), p.2211-2213
1. Verfasser: Quilodrán, René
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Codes
Polynomials
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Zusammenfassung:We show that given a collection of $A$ lines in $\mathbb{R}^n$, $n\geq2$, the maximum number of their joints (points incident to at least $n$ lines whose directions form a linearly independent set) is $O(A^{n/(n-1)})$. An analogous result for smooth algebraic curves is also proven.
ISSN:0895-4801
1095-7146
DOI:10.1137/090763160