On the equivalence of certain quasi-Hermitian varieties

IF 0.5 4区数学 Q3 MATHEMATICS Journal of Combinatorial Designs Pub Date : 2022-12-07 DOI:10.1002/jcd.21870

Angela Aguglia, Luca Giuzzi

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引用次数: 3

Abstract

By Aguglia et al., new quasi-Hermitian varieties $ℳ_{α, β}$ in $PG (r, q^{2})$ depending on a pair of parameters $α, β$ from the underlying field $GF (q^{2})$ have been constructed. In the present paper we study the structure of the lines contained in $ℳ_{α, β}$ and consequently determine the projective equivalence classes of such varieties for $q$ odd and $r = 3$ . As a byproduct, we also prove that the collinearity graph of $ℳ_{α, β}$ is connected with diameter 3 for $q \equiv 1 (\mod 4)$ .

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关于某些拟Hermitian变种的等价性

由Aguglia等人，新的准埃尔米特品种ℳα，PG中的β$（r，q2）$\text｛PG｝（r，｛q｝^｛2｝）$取决于一对参数α，β$\alpha，\已经构造了来自底层字段GF（q2）$\text｛GF｝（｛q｝^｛2｝）$的beta$。本文研究了ℳα，β$｛\rm｛\mathcal M｝｝}｝_｛\alpha，\beta｝$，并因此确定q$q$odd和r的此类变体的投影等价类=3$r=3$。作为副产品，我们还证明了ℳα，β${｛\rm｛\mathcal M｝｝}｝_｛\alpha，\beta｝$与直径3相连（mod 4）$q\equiv 1\，（\mathrm｛mod｝\，4）$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Combinatorial Designs 数学-数学

CiteScore

1.60

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Combinatorial Designs is an international journal devoted to the timely publication of the most influential papers in the area of combinatorial design theory. All topics in design theory, and in which design theory has important applications, are covered, including: block designs, t-designs, pairwise balanced designs and group divisible designs Latin squares, quasigroups, and related algebras computational methods in design theory construction methods applications in computer science, experimental design theory, and coding theory graph decompositions, factorizations, and design-theoretic techniques in graph theory and extremal combinatorics finite geometry and its relation with design theory. algebraic aspects of design theory. Researchers and scientists can depend on the Journal of Combinatorial Designs for the most recent developments in this rapidly growing field, and to provide a forum for both theoretical research and applications. All papers appearing in the Journal of Combinatorial Designs are carefully peer refereed.