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# An Erdos-Ko-Rado theorem for finite classical polar spaces

Klaus Metsch (UGent)
(2016) 43(2). p.375-397
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Organization
Abstract
Consider a finite classical polar space of rank d >= 2 and an integer n with 0 < n < d. In this paper, it is proved that the set consisting of all subspaces of rank n that contain a given point is a largest Erdos-Ko-Rado set of subspaces of rank n of the polar space. We also show that there are no other Erdos-Ko-Rado sets of subspaces of rank n of the same size.
Keywords
Erdos-Ko-Rado set, Polar space, Weighted Hoffman's bound, INTERSECTION THEOREMS, EIGENVALUE BOUNDS, SETS, SYSTEMS

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## Citation

Chicago
Metsch, Klaus. 2016. “An Erdos-Ko-Rado Theorem for Finite Classical Polar Spaces.” Journal of Algebraic Combinatorics 43 (2): 375–397.
APA
Metsch, K. (2016). An Erdos-Ko-Rado theorem for finite classical polar spaces. JOURNAL OF ALGEBRAIC COMBINATORICS, 43(2), 375–397.
Vancouver
1.
Metsch K. An Erdos-Ko-Rado theorem for finite classical polar spaces. JOURNAL OF ALGEBRAIC COMBINATORICS. 2016;43(2):375–97.
MLA
Metsch, Klaus. “An Erdos-Ko-Rado Theorem for Finite Classical Polar Spaces.” JOURNAL OF ALGEBRAIC COMBINATORICS 43.2 (2016): 375–397. Print.
```@article{8033721,
abstract     = {Consider a finite classical polar space of rank d {\textrangle}= 2 and an integer n with 0 {\textlangle} n {\textlangle} d. In this paper, it is proved that the set consisting of all subspaces of rank n that contain a given point is a largest Erdos-Ko-Rado set of subspaces of rank n of the polar space. We also show that there are no other Erdos-Ko-Rado sets of subspaces of rank n of the same size.},
author       = {Metsch, Klaus},
issn         = {0925-9899},
journal      = {JOURNAL OF ALGEBRAIC COMBINATORICS},
keyword      = {Erdos-Ko-Rado set,Polar space,Weighted Hoffman's bound,INTERSECTION THEOREMS,EIGENVALUE BOUNDS,SETS,SYSTEMS},
language     = {eng},
number       = {2},
pages        = {375--397},
title        = {An Erdos-Ko-Rado theorem for finite classical polar spaces},
url          = {http://dx.doi.org/10.1007/s10801-015-0637-7},
volume       = {43},
year         = {2016},
}

```
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