On the number of small Steiner triple systems with Veblen points

IF 0.7 3区数学 Q2 MATHEMATICS Discrete Mathematics Pub Date : 2024-10-21 DOI:10.1016/j.disc.2024.114294

引用次数: 0

Abstract

The concept of Schreier extensions of loops was introduced in the general case in [11] and, more recently, it has been explored in the context of Steiner loops in [6]. In the latter case, it gives a powerful method for constructing Steiner triple systems containing Veblen points. Counting all Steiner triple systems of order v is an open problem for

v > 21

. In this paper, we investigate the number of Steiner triple systems of order 19, 27 and 31 containing Veblen points and we present some examples.

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关于具有维布伦点的小型斯坦纳三重系统的数量

在一般情况下，[11] 引入了循环的施赖尔扩展概念，最近，[6] 又在斯坦纳循环的背景下对其进行了探索。在后一种情况下，它为构建包含维布伦点的斯坦纳三重系统提供了一种强有力的方法。对于 v>21 而言，计算所有 v 阶的斯坦纳三重系统是一个未决问题。在本文中，我们研究了含有 Veblen 点的 19、27 和 31 阶 Steiner 三重系统的数量，并给出了一些示例。

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

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.