The Hilton-Milner theorem for finite affine spaces

Guo Jun

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The Hilton-Milner theorem for finite affine spaces

机译：有限仿射空间的Hilton-Milner定理

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摘要

Suppose 3 = 2k + 1 n. Let AG(n, F-q) be the n-dimensional affine space over the finite field F-q and M(k,n) be the set of all k-flats in AG(n,F-q). Suppose that F subset of M(k, n) is an intersecting family with boolean AND(F is an element of F), F = (empty set). In this paper, we show vertical bar F vertical bar = 1 + [(n-1)(k-1)](q) + Sigma(k-1)(i=0) q(i(i+1)) )(q(k-i) - 1)[(n-1-k)(i)](q) [(k)(i)](q), and describe the structure of F which reaches this bound. (C) 2018 Elsevier Inc. All rights reserved.

机译：假设3 <= 2k + 1

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来源
《Finite fields and their applications》 |2019年第1期|151-166|共16页
作者
Guo Jun;
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作者单位

Langfang Normal Univ, Coll Math & Informat Sci, Langfang 065000, Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Hilton-Milner theorem; Intersecting family; Affine space; Flat;

机译：希尔顿·米尔纳定理;相交家庭;仿射空间;平面;

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专利

1. A Hilton-Milner Theorem for Vector Spaces [J] . A. Blokhuis, A. E. Brouwer, A. Chowdhury, Electronic Journal Of Combinatorics . 2010,第1期

机译：向量空间的希尔顿-米尔纳定理
2. The Erdos-Ko-Rado theorem for finite affine spaces [J] . Guo Jun, Xu Qiuli Linear & Multilinear Algebra: An International Journal Publishing Articles, Reviews and Problems . 2017,第1a3期

机译：用于有限染色条件的Erdos-Ko-rado定理
3. Lattices associated with finite vector spaces and finite affine spaces [J] . Guo J Ars Combinatoria: An Australian-Canadian Journal of Combinatorics . 2008,第Null期

机译：与有限向量空间和有限仿射空间相关的格
4. Convergence theorems for a finite family of strictly asymptotically pseudo-contractive mappings in q-uniformly smooth Banach spaces [C] . Huancheng Zhang, Aimin Yang, Yamian Peng, International Conference on Intelligent Structure and Vibration Control . 2011

机译：Q-均匀平滑的Banach空间中严格渐近伪收缩映射的有限家庭的融合定理
5. CONSTANT TERM IDENTITIES FOR FINITE AND AFFINE ROOT SYSTEMS: CONJECTURES AND THEOREMS. [D] . MORRIS, WALTER GARFIELD, II. 1982

机译：有限和仿射根系统的常数项：假想和定理。
6. Strong Convergence Theorems for a Common Fixed Point of a Finite Family of Bregman Weak Relativity Nonexpansive Mappings in Reflexive Banach Spaces [O] . Habtu Zegeye, Naseer Shahzad -1

机译：自反Banach空间中Bregman弱相对论非扩张映射的有限个族的公共不动点的强收敛定理
7. A Hilton-Milner Theorem for Vector Spaces [O] . A. Blokhuis, A. E. Brouwer, A. Chowdhury, 2010

机译：矢量空间的希尔顿米尔纳定理

The Hilton-Milner theorem for finite affine spaces

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