Intersection sizes of linear subspaces with the hypercube

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:170

Article

Groenland, Carla¹  Johnston, Tom¹ 

[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England

关键词: Linear subspace;    Intersection;    Hypercube;   

DOI  :  10.1016/j.jcta.2019.105142

来源: Elsevier

【 摘 要 】

We continue the study by Melo and Winter (2019) [3] on the possible intersection sizes of a k-dimensional subspace with the vertices of the n-dimensional hypercube in Euclidean space. Melo and 'Winter conjectured that all intersection sizes larger than 2(k-1) (the large sizes) are of the form 2(k-1) + 2(i). We show that this is almost true: the large intersection sizes are either of this form or of the form 35.2(k-6). We also disprove a second conjecture of Melo and Winter by proving that a positive fraction of the small values is missing. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free