Intersection theorems for systems of finite vector spaces

Hsieh, Wan-Hsin

doi:10.1016/0012-365x(75)90091-6

Cited by 104 publications

(70 citation statements)

References 5 publications

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“…The celebrated Erdös-Ko-Rado theorem determines the maximum size of such family. The q-analog problem was considered for subspaces in [20,13]. For the q-analog problem, a t-intersecting family is is a set of k-subspaces whose pairwise intersection is at least t. In [13] it was proved that Theorem 2.…”

Section: + 1 Codewords Then the Code Is A Sunflowermentioning

confidence: 99%

Equidistant codes in the Grassmannian

Etzion

Raviv

2015

Discrete Applied Mathematics

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Equidistant codes over vector spaces are considered. For k-dimensional subspaces over a large vector space the largest code is always a sunflower. We present several simple constructions for such codes which might produce the largest non-sunflower codes. A novel construction, based on the Plücker embedding, for 1-intersecting codes of k-dimensional subspaces over F n q , n ≥ k+1 2 , where the code size isis presented. Finally, we present a related construction which generates equidistant constant rank codes with matrices of size n × n 2 over F q , rank n − 1, and rank distance n − 1.

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Section: + 1 Codewords Then the Code Is A Sunflowermentioning

confidence: 99%

Equidistant codes in the Grassmannian

Etzion

Raviv

2015

Discrete Applied Mathematics

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“…In 1975, Hsieh [41] proved the q-analogue of the theorem of Erdős, Ko and Rado for 2k + 1 ≤ n. Greene and Kleitman [34] found an elegant proof for the case where k | n, settling the missing n = 2k case. Combining their results gives that the size of a maximum size coclique in qK n:k is at most n−1 k−1 for n ≥ 2k.…”

Section: Vector Spacesmentioning

confidence: 99%

On q-analogues and stability theorems

et al. 2011

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Abstract. In this survey recent results about q-analogues of some classical theorems in extremal set theory are collected. They are related to determining the chromatic number of the q-analogues of Kneser graphs. For the proof one needs results on the number of 0-secant subspaces of point sets, so in the second part of the paper recent results on the structure of point sets having few 0-secant subspaces are discussed. Our attention is focussed on the planar case, where various stability results are given.Mathematics Subject Classification (2010). 05D05, 05B25.

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“…The following result is due to Hsieh [8] (his proof does not cover the case v = 2k + 1, q = 2). Our proof is new, and considerably simpler.…”

Section: Q-kneser Graphsmentioning

confidence: 99%

Independent Sets In Association Schemes

Godsil

Newman

2006

Combinatorica

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Let X be k-regular graph on v vertices and let τ denote the least eigenvalue of its adjacency matrix A(X). If α(X) denotes the maximum size of an independent set in X, we have the following well known bound:It is less well known that if equality holds here and S is a maximum independent set in X with characteristic vector x, then the vectoris an eigenvector for A(X) with eigenvalue τ . In this paper we show how this can be used to characterise the maximal independent sets in certain classes of graphs. As a corollary we show that a graph defined on the partitions of {1, . . . , 9} with three cells of size three is a core. * Research supported by NSERC.

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Intersection theorems for systems of finite vector spaces

Cited by 104 publications

References 5 publications

Equidistant codes in the Grassmannian

Equidistant codes in the Grassmannian

On q-analogues and stability theorems

Independent Sets In Association Schemes

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