vector space partitions
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Author(s):  
Thomas Honold ◽  
Michael Kiermaier ◽  
Sascha Kurz


2012 ◽  
Vol 04 (01) ◽  
pp. 1250001 ◽  
Author(s):  
OLOF HEDEN

A vector space partition is here a collection [Formula: see text] of subspaces of a finite vector space V(n, q), of dimension n over a finite field with q elements, with the property that every non-zero vector is contained in a unique member of [Formula: see text]. Vector space partitions relate to finite projective planes, design theory and error correcting codes. In the first part of the paper I will discuss some relations between vector space partitions and other branches of mathematics. The other part of the paper contains a survey of known results on the type of a vector space partition, more precisely: the theorem of Beutelspacher and Heden on T-partitions, rather recent results of El-Zanati et al. on the different types that appear in the spaces V(n, 2), for n ≤ 8, a result of Heden and Lehmann on vector space partitions and maximal partial spreads including their new necessary condition for the existence of a vector space partition, and furthermore, I will give a theorem of Heden on the length of the tail of a vector space partition. Finally, I will also give a few historical remarks.



2012 ◽  
Vol 312 (2) ◽  
pp. 351-361 ◽  
Author(s):  
Juliane Lehmann ◽  
Olof Heden


2008 ◽  
Vol 48 (1) ◽  
pp. 69-77 ◽  
Author(s):  
A. D. Blinco ◽  
S. I. El-Zanati ◽  
G. F. Seelinger ◽  
P. A. Sissokho ◽  
L. E. Spence ◽  
...  


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