On finite models of Hilbert's incidence geometry

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-07-22 DOI:10.1016/j.disc.2024.114159

Kristina Ago, Bojan Bašić, Milica Maksimović, Milica Šobot

引用次数: 0

Abstract

We consider finite models of the first group of Hilbert's axioms of the Euclidean geometry (the so-called axioms of incidence). We give a lower bound on the number of such models with n points, and we calculate their exact number for n up to 12.

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论希尔伯特入射几何的有限模型

我们考虑欧几里得几何希尔伯特公理第一组的有限模型（即所谓的入射公理）。我们给出了带有点的此类模型数量的下限，并计算了最多 12 个模型的精确数量。

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.