A hilton-milner theorem for vector spaces

A. Blokhuis; A. E. Brouwer; A. Chowdhury; P. Frankl; T. Mussche; B. Patkós; T. Szonyi

doi:10.37236/343

A hilton-milner theorem for vector spaces

A. Blokhuis, A. E. Brouwer, A. Chowdhury, P. Frankl, T. Mussche, B. Patkós, T. Szonyi

Research output: Contribution to journal › Article › peer-review

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Abstract

We show for k > 2 that if q > 3 and n > 2k + 1, or q = 2 and n > 2k + 2, then any intersecting family F of k-subspaces of an n-dimensional vector space over GF(q) with f]_Fe:FF = 0 has size at most [ⁿ_kz₁¹] - q^k(k~^{1) n}_k^k₁¹] + 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.

Original language	English (US)
Pages (from-to)	1-12
Number of pages	12
Journal	Electronic Journal of Combinatorics
Volume	17
Issue number	1
DOIs	https://doi.org/10.37236/343
State	Published - 2010
Externally published	Yes

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T1 - A hilton-milner theorem for vector spaces

AU - Blokhuis, A.

AU - Brouwer, A. E.

AU - Chowdhury, A.

AU - Frankl, P.

AU - Mussche, T.

AU - Patkós, B.

AU - Szonyi, T.

PY - 2010

Y1 - 2010

N2 - We show for k > 2 that if q > 3 and n > 2k + 1, or q = 2 and n > 2k + 2, then any intersecting family F of k-subspaces of an n-dimensional vector space over GF(q) with f]Fe:FF = 0 has size at most [nkz11] - qk(k~1) nkk11] + qk. 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.

AB - We show for k > 2 that if q > 3 and n > 2k + 1, or q = 2 and n > 2k + 2, then any intersecting family F of k-subspaces of an n-dimensional vector space over GF(q) with f]Fe:FF = 0 has size at most [nkz11] - qk(k~1) nkk11] + qk. 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.

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A hilton-milner theorem for vector spaces

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