Absorbing homogeneous polynomials arising from rational homotopy theory and graph theory

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-12-14 DOI:10.1007/s00200-022-00591-2

Mahmoud Benkhalifa

引用次数: 0

Abstract

An ideal \({{\mathcal {I}}}\) of \({\mathbb {Q}}[x_1,\dots ,x_n]\) is said to be m-absorbing if any monomial of total degree \(p>m\) belongs to \({{\mathcal {I}}}\) and if there is a monomial M of total degree m such that \(M\not \in {{\mathcal {I}}}.\) Inspired by the fundamental work of Lechuga and Murillo (Topology 39:89–94, 2000) who established a connection between graph theory and rational homotopy theory, these paper aims to characterise the m-absorbing ideals of \({\mathbb {Q}}[x_1,\dots ,x_n]\) generated by a family of complete homogeneous symmetric polynomials of the form \(P^{(k)}_{rs}=\sum _{t=1}^{k}x^{k-t}_{r}x^{t-1}_{s}\), where \(k\ge 3.\)

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吸收有理同伦论和图论中的齐次多项式

如果任何总度数为 \(p>m\) 的单项式都属于 \({{mathcal {I}}}})，并且如果存在一个总度数为 m 的单项式 M，使得 \(M\not\in {{mathcal {I}}}})的理想 \({{mathcal {I}}})被称为 m-吸收。\受 Lechuga 和 Murillo 的基础工作启发（Topology 39：89-94, 2000）在图论和理性同调理论之间建立了联系，本文旨在描述 \({\mathbb {Q}}[x_1、\dots ,x_n]\) 由形式为 \(P^{(k)}_{rs}=\sum _{t=1}^{k}x^{k-t}_{r}x^{t-1}_{s}\) 的完全同构对称多项式族生成，其中 \(k\ge 3.\)

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

Applicable Algebra in Engineering Communication and Computing 工程技术-计算机：跨学科应用

CiteScore

2.90

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems. Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology. Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal. On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.