Cameron-Liebler sets for maximal totally isotropic flats in classical affine spaces

被引：1

作者：

Guo, Jun ^{[1
]}

Wan, Lingyu ^{[1
]}

机构：

[1] Langfang Normal Univ, Dept Math, Langfang 065000, Peoples R China

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2023年 / 31卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Cameron-Liebler set; classical affine space; maximal totally isotropic flat; LINE CLASSES; ASSOCIATION SCHEMES; ORBITS;

D O I：

10.1002/jcd.21909

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let ACG(2 & nu;,Fq) $ACG(2\nu ,{{\mathbb{F}}}_{q})$ be the 2 & nu; $2\nu $-dimensional classical affine space with parameter e $e$ over a q $q$-element finite field Fq ${{\mathbb{F}}}_{q}$, and O & nu; ${{\mathscr{O}}}_{\nu }$ be the set of all maximal totally isotropic flats in ACG(2 & nu;,Fq) $ACG(2\nu ,{{\mathbb{F}}}_{q})$. In this paper, we discuss Cameron-Liebler sets in O & nu; ${{\mathscr{O}}}_{\nu }$, obtain several equivalent definitions and present some classification results.

引用

页码：547 / 574

页数：28

共 22 条

[1] Cameron-Liebler sets of generators in finite classical polar spaces
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[6] Cameron-Liebler sets in bilinear forms graphs
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[7] The graphs induced by maximal totally isotropic flats of affine-unitary spaces
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[8] A modular equality for Cameron-Liebler line classes in projective and affine spaces of odd dimension
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[10] Equivalent definitions for (degree one) Cameron-Liebler classes of generators in finite classical polar spaces
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