The concavity property of some array of numbers (Q2767620)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The concavity property of some array of numbers |
scientific article; zbMATH DE number 1698080
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The concavity property of some array of numbers |
scientific article; zbMATH DE number 1698080 |
Statements
30 January 2002
0 references
concavity property
0 references
array of numbers
0 references
vector space
0 references
finite field
0 references
\(k\)-dimensional subspaces
0 references
0 references
0.83589804
0 references
0 references
0.8217358
0 references
The concavity property of some array of numbers (English)
0 references
The authors prove that for all integers \(k\) with \(1\leq k\leq n+1,\;n=0,1,2,\ldots\) NEWLINE\[NEWLINE\left(\left[\left.\begin{matrix} n+1\\ k\end{matrix}\right|1\right]\right)^2>\left[\left.\begin{matrix} n+1\\ k-1\end{matrix}\right|1\right]\left[\left.\begin{matrix} n+1\\ k+1\end{matrix}\right|1\right],NEWLINE\]NEWLINE where \(\left[\left.\begin{matrix} d\\ p\end{matrix}\right|1\right]=0\) if either \(p=0\) or \(p>d\). Here \(\left[\left.\begin{matrix} n\\ k\end{matrix}\right|1\right]\) is the number of all pairwise different unit-weight \(k\)-dimensional subspaces of the \(n\)-dimensional vector space over a finite field.
0 references
