3-强制2-结构

IF 0.6 Q4 MATHEMATICS, APPLIED

Discrete Mathematics Algorithms and Applications Pub Date : 2023-10-18 DOI:10.1142/s1793830923500866

Abderrahim Boussairi, Pierre Ille

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引用次数: 0

摘要

给定集合[公式:见文]和[公式:见文]，标记的2-结构是一个函数[公式:见文]从[公式:见文]到[公式:见文]。集合[公式:见文]称为[公式:见文]的顶点集，用[公式:见文]表示。[Formula: see text]的标签集是[Formula: see text]的集合[Formula: see text]，使得[Formula: see text]对于某些[Formula: see text]。给定[公式:见文]，[公式:见文]的二子结构[公式:见文]用[公式:见文]表示。[Formula: see text]的对偶[Formula: see text]在[Formula: see text]上定义如下。对于不同的[公式:见文]，[公式:见文]。标记的2-结构[公式:见文]是可逆的，前提是[公式:见文]使[公式:见文]和[公式:见文]，如果[公式:见文]，则[公式:见文]。我们只考虑顶点集有限的可逆标记2结构。设[公式:见文]和[公式:见文]为两个结构，这样[公式:见文]。给定[公式:见文]，[公式:见文]和[公式:见文]是[公式:见文]-半同构，如果对于每一个[公式:见文]，使得[公式:见文]，[公式:见文]与[公式:见文]或[公式:见文]同构。此外，设[公式:见文本]为双结构。给定[公式:见文]，[公式:见文]是[公式:见文]-强制如果[公式:见文]和[公式:见文]是唯一的2-结构[公式:见文]-半同态[公式:见文]。我们描述了[公式:见文本]-强制2结构。最后，我们提供了一大类[公式:见文本]-强制2结构。

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The 3-forced 2-structures

Given sets [Formula: see text] and [Formula: see text], a labeled 2-structure is a function [Formula: see text] from [Formula: see text] to [Formula: see text]. The set [Formula: see text] is called the vertex set of [Formula: see text] and denoted by [Formula: see text]. The label set of [Formula: see text] is the set [Formula: see text] of [Formula: see text] such that [Formula: see text] for some [Formula: see text]. Given [Formula: see text], the 2-substructure [Formula: see text] of [Formula: see text] is denoted by [Formula: see text]. The dual [Formula: see text] of [Formula: see text] is defined on [Formula: see text] as follows. For distinct [Formula: see text], [Formula: see text]. A labeled 2-Structure [Formula: see text] is reversible provided that for [Formula: see text] such that [Formula: see text] and [Formula: see text], if [Formula: see text], then [Formula: see text]. We only consider reversible labeled 2-structures whose vertex set is finite. Let [Formula: see text] and [Formula: see text] be 2-structures such that [Formula: see text]. Given [Formula: see text], [Formula: see text] and [Formula: see text] are [Formula: see text]-hemimorphic if for every [Formula: see text] such that [Formula: see text], [Formula: see text] is isomorphic to [Formula: see text] or [Formula: see text]. Furthermore, let [Formula: see text] be a 2-structure. Given [Formula: see text], [Formula: see text] is [Formula: see text]-forced if [Formula: see text] and [Formula: see text] are the only 2-structures [Formula: see text]-hemimorphic to [Formula: see text]. We characterize the [Formula: see text]-forced 2-structures. Last, we provide a large class of [Formula: see text]-forced 2-structures.

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来源期刊

Discrete Mathematics Algorithms and Applications MATHEMATICS, APPLIED-

CiteScore

1.50

自引率

41.70%

发文量

129