Analogues for Sperner and Erdös-Ko-Rado Theorems For Subspaces of Linear Spaces

Gil Kalai

doi:10.1016/S0167-5060(08)70049-9

Analogues for Sperner and Erdös-Ko-Rado Theorems For Subspaces of Linear Spaces

Gil Kalai^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

3 Scopus citations

Abstract

Abstract: Theorem A. Let (V₁, W₁), (V₂, W₂), ..., (V_m, W_m) be m pairs of subspaces of n-dimensional vector Fⁿ such that:. (a) V_i ∩W_i, = {0} for 1 ≤i ≤m;. (b) V_i, ∩W_i, ≠ {0} for 1 ≤i ≠ i ≤m. Then m ≤({black small square}). If moreover, dim V_i≤k ≤ n/2 for i = 1, 2, ..., m, then m ≤({black small square}). Theorem B. Let (V₁ W₁), ..., (V_m, W_m) be m-pairs of subspaces of Fⁿ, satisfying (a), (b) of the previous theorem and:. (c) dim V_i = k ≤ n/2,. (d) dim (V_i ∩ V_i) ≤ 1 for 1 ≤i ≠ j≤ m, then m≤ ({black small square}).

Original language	English
Pages (from-to)	135
Number of pages	1
Journal	Annals of Discrete Mathematics
Volume	9
Issue number	C
DOIs	https://doi.org/10.1016/S0167-5060(08)70049-9
State	Published - 1980

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@article{503ba52170c64366a37527ab8e0e576e,

title = "Analogues for Sperner and Erd{\"o}s-Ko-Rado Theorems For Subspaces of Linear Spaces",

abstract = "Abstract: Theorem A. Let (V1, W1), (V2, W2), ..., (Vm, Wm) be m pairs of subspaces of n-dimensional vector Fn such that:. (a) Vi ∩Wi, = \{0\} for 1 ≤i ≤m;. (b) Vi, ∩Wi, ≠ \{0\} for 1 ≤i ≠ i ≤m. Then m ≤(\{black small square\}). If moreover, dim Vi≤k ≤ n/2 for i = 1, 2, ..., m, then m ≤(\{black small square\}). Theorem B. Let (V1 W1), ..., (Vm, Wm) be m-pairs of subspaces of Fn, satisfying (a), (b) of the previous theorem and:. (c) dim Vi = k ≤ n/2,. (d) dim (Vi ∩ Vi) ≤ 1 for 1 ≤i ≠ j≤ m, then m≤ (\{black small square\}).",

author = "Gil Kalai",

year = "1980",

doi = "10.1016/S0167-5060(08)70049-9",

language = "אנגלית",

volume = "9",

pages = "135",

journal = "Annals of Discrete Mathematics",

issn = "0167-5060",

publisher = "Elsevier B.V.",

number = "C",

}

TY - JOUR

T1 - Analogues for Sperner and Erdös-Ko-Rado Theorems For Subspaces of Linear Spaces

AU - Kalai, Gil

PY - 1980

Y1 - 1980

N2 - Abstract: Theorem A. Let (V1, W1), (V2, W2), ..., (Vm, Wm) be m pairs of subspaces of n-dimensional vector Fn such that:. (a) Vi ∩Wi, = {0} for 1 ≤i ≤m;. (b) Vi, ∩Wi, ≠ {0} for 1 ≤i ≠ i ≤m. Then m ≤({black small square}). If moreover, dim Vi≤k ≤ n/2 for i = 1, 2, ..., m, then m ≤({black small square}). Theorem B. Let (V1 W1), ..., (Vm, Wm) be m-pairs of subspaces of Fn, satisfying (a), (b) of the previous theorem and:. (c) dim Vi = k ≤ n/2,. (d) dim (Vi ∩ Vi) ≤ 1 for 1 ≤i ≠ j≤ m, then m≤ ({black small square}).

AB - Abstract: Theorem A. Let (V1, W1), (V2, W2), ..., (Vm, Wm) be m pairs of subspaces of n-dimensional vector Fn such that:. (a) Vi ∩Wi, = {0} for 1 ≤i ≤m;. (b) Vi, ∩Wi, ≠ {0} for 1 ≤i ≠ i ≤m. Then m ≤({black small square}). If moreover, dim Vi≤k ≤ n/2 for i = 1, 2, ..., m, then m ≤({black small square}). Theorem B. Let (V1 W1), ..., (Vm, Wm) be m-pairs of subspaces of Fn, satisfying (a), (b) of the previous theorem and:. (c) dim Vi = k ≤ n/2,. (d) dim (Vi ∩ Vi) ≤ 1 for 1 ≤i ≠ j≤ m, then m≤ ({black small square}).

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DO - 10.1016/S0167-5060(08)70049-9

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AN - SCOPUS:77957760766

SN - 0167-5060

VL - 9

SP - 135

JO - Annals of Discrete Mathematics

JF - Annals of Discrete Mathematics

IS - C

ER -

Analogues for Sperner and Erdös-Ko-Rado Theorems For Subspaces of Linear Spaces

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