A Hilton-Milner theorem for vector spaces
The electronic journal of combinatorics, Tome 17 (2010)
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Zbl EuDML
We show for $k \geq 2$ that if $q\geq 3$ and $n \geq 2k+1$, or $q=2$ and $n \geq 2k+2$, then any intersecting family ${\cal F}$ of $k$-subspaces of an $n$-dimensional vector space over $GF(q)$ with $\bigcap_{F \in {\cal F}} F=0$ has size at most $\left[{n-1\atop k-1}\right]-q^{k(k-1)}\left[{n-k-1\atop k-1}\right]+q^k$. This bound is sharp as is shown by Hilton-Milner type families. As an application of this result, we determine the chromatic number of the corresponding $q$-Kneser graphs.
A. Blokhuis; A. E. Brouwer; A. Chowdhury; P. Frankl; T. Mussche; B. Patkós; T. Szőnyi. A Hilton-Milner theorem for vector spaces. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/343
@article{10_37236_343,
author = {A. Blokhuis and A. E. Brouwer and A. Chowdhury and P. Frankl and T. Mussche and B. Patk\'os and T. Sz\H{o}nyi},
title = {A {Hilton-Milner} theorem for vector spaces},
journal = {The electronic journal of combinatorics},
year = {2010},
volume = {17},
doi = {10.37236/343},
zbl = {1189.05171},
url = {http://geodesic.mathdoc.fr/articles/10.37236/343/}
}
TY - JOUR AU - A. Blokhuis AU - A. E. Brouwer AU - A. Chowdhury AU - P. Frankl AU - T. Mussche AU - B. Patkós AU - T. Szőnyi TI - A Hilton-Milner theorem for vector spaces JO - The electronic journal of combinatorics PY - 2010 VL - 17 UR - http://geodesic.mathdoc.fr/articles/10.37236/343/ DO - 10.37236/343 ID - 10_37236_343 ER -
%0 Journal Article %A A. Blokhuis %A A. E. Brouwer %A A. Chowdhury %A P. Frankl %A T. Mussche %A B. Patkós %A T. Szőnyi %T A Hilton-Milner theorem for vector spaces %J The electronic journal of combinatorics %D 2010 %V 17 %U http://geodesic.mathdoc.fr/articles/10.37236/343/ %R 10.37236/343 %F 10_37236_343
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