Dividing and forking in random hypergraphs

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2024-09-24 DOI:10.1016/j.apal.2024.103521

Hirotaka Kikyo , Akito Tsuboi

引用次数: 0

Abstract

We investigate the class of m-hypergraphs in which substructures with l elements have more than s subsets of size m that do not form a hyperedge. The class has a (unique) Fraïssé limit, if

0 \leq s < (\begin{matrix} l - 2 \\ m - 2 \end{matrix})

. We show that the theory of the Fraïssé limit has SU-rank one if

0 \leq s < (\begin{matrix} l - 3 \\ m - 3 \end{matrix})

, and dividing and forking will be different concepts in the theory if

(\begin{matrix} l - 3 \\ m - 3 \end{matrix}) \leq s < (\begin{matrix} l - 2 \\ m - 2 \end{matrix})

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随机超图中的分割和分叉

我们研究了 m-hypergraphs 类，在这类图中，有 l 个元素的子结构有多于 s 个大小为 m 的子集不构成一个 hyperedge。如果0≤s<(l-2m-2)，则该类图具有（唯一的）弗雷泽极限。我们证明，如果 0≤s<(l-3m-3), 那么弗拉伊塞极限理论具有 SU-rank one，如果 (l-3m-3)≤s<(l-2m-2), 那么分割和分叉在理论中将是不同的概念。

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

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.