On regular systems of finite classical polar spaces

被引：2

作者：

Cossidente, Antonio ^{[1
]}

Marino, Giuseppe ^{[2
]}

Pavese, Francesco ^{[3
]}

Smaldore, Valentino ^{[1
]}

机构：

[1] Univ Basilicata, Dipartimento Matemat Informat Econ, I-85100 Potenza, Italy

[2] Univ Napoli Federico II, Dipartimento Matemat & Applicaz Renato Caccioppol, Cupa Nuova Cintia 21, I-80126 Naples, Italy

[3] Politecn Bari, Dipartimento Meccan Matemat & Management, Via Orabona 4, I-70125 Bari, Italy

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2022年 / 100卷

关键词：

MAXIMAL-SUBGROUPS; M-OVOIDS; GENERALIZED QUADRANGLE; ASSOCIATION SCHEMES; STABILIZING SPREADS; FIELD REDUCTION; HEMISYSTEMS; SETS; CONSTRUCTIONS; FAMILY;

D O I：

10.1016/j.ejc.2021.103439

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let P be a finite classical polar space of rank d. An m-regular system with respect to (k - 1)-dimensional projective spaces of P, 1 <= k <= d - 1, is a set R of generators of P with the property that every (k - 1)-dimensional projective space of P lies on exactly m generators of R. Regular systems of polar spaces are investigated. Some non-existence results about certain 1-regular systems of polar spaces with low rank are proved and a procedure to obtain m'-regular systems from a given m-regular system is described. Finally, three different construction methods of regular systems w.r.t. points of various polar spaces are discussed. (C) 2021 Elsevier Ltd. All rights reserved.

引用

页数：20

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