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

共 50 条

[21] On m-ovoids of finite classical polar spaces with an irreducible transitive automorphism group
Feng, Tao
Li, Weicong
Tao, Ran
SCIENCE CHINA-MATHEMATICS, 2024, 67 (03) : 683 - 712
[22] The largest Erdős-Ko-Rado sets of planes in finite projective and finite classical polar spaces
Maarten De Boeck
Designs, Codes and Cryptography, 2014, 72 : 77 - 117
[23] INFORMATION GEOMETRY IN FUNCTIONAL SPACES OF CLASSICAL AND QUANTUM FINITE STATISTICAL SYSTEMS
INGARDEN, RS
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 1981, 19 (12) : 1609 - 1633
[24] FINITE REGULAR LOCALLY PROJECTIVE SPACES
DOYEN, J
HUBAUT, X
MATHEMATISCHE ZEITSCHRIFT, 1971, 119 (01) : 83 - &
[25] Cross-Intersecting Erclos-Ko-Rado Sets in Finite Classical Polar Spaces
Ihringer, Ferdinand
ELECTRONIC JOURNAL OF COMBINATORICS, 2015, 22 (02):
[26] Lax embeddings of polar spaces in finite projective spaces
Thas, JA
Van Maldeghem, H
FORUM MATHEMATICUM, 1999, 11 (03) : 349 - 367
[27] Dimensional dual hyperovals in classical polar spaces
John Sheekey
Designs, Codes and Cryptography, 2016, 80 : 415 - 420
[28] Dimensional dual hyperovals in classical polar spaces
Sheekey, John
DESIGNS CODES AND CRYPTOGRAPHY, 2016, 80 (02) : 415 - 420
[29] Regular sets of lines in rank 3 polar spaces
Ihringer, Ferdinand
Rodgers, Morgan
FINITE FIELDS AND THEIR APPLICATIONS, 2025, 103
[30] On codewords in the dual code of classical generalised quadrangles and classical polar spaces
Pepe, Valentina
Storme, Leo
Van de Voorde, Geertrui
DISCRETE MATHEMATICS, 2010, 310 (22) : 3132 - 3148

← 1 2 3 4 5 →