有限二维非加法测量的基本抵消违反序列集

IF 0.4 Q4 MATHEMATICS

Annales Mathematicae Silesianae Pub Date : 2023-12-13 DOI:10.2478/amsil-2023-0023

Che Tat Ng

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引用次数: 0

摘要

摘要取消条件在有限二维笛卡尔积集 X 上弱阶的测量表示理论中起着核心作用。当且仅当弱阶不违反取消条件时，它才具有可加表示性。给定 X，一个长期悬而未决的问题是确定每一个不可加表示的线性阶都违反的最简单的取消条件集。在此，我们报告了关于 5 乘 5 积 X 的最简单的取消条件集。

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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A Basic Set of Cancellation Violating Sequences for Finite Two-Dimensional Non-Additive Measurement

Abstract Cancellation conditions play a central role in the representation theory of measurement for a weak order on a finite two-dimensional Cartesian product set X. A weak order has an additive representation if and only if it violates no cancellation conditions. Given X, a longstanding open problem is to determine the simplest set of cancellation conditions that is violated by every linear order that is not additively representable. Here, we report that the simplest set of cancellation conditions on a 5 by 5 product X is obtained.

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来源期刊

Annales Mathematicae Silesianae Mathematics-Mathematics (all)

CiteScore

0.60

自引率

25.00%

发文量

审稿时长

27 weeks