Absorbing homogeneous polynomials arising from rational homotopy theory and graph theory

An ideal I of Q [ x 1 , ⋯ , x n ] is said to be m -absorbing if any monomial of total degree p > m belongs to I and if there is a monomial M of total degree m such that M ∉ I . Inspired by the fundamental work of Lechuga and Murillo (Topology 39:89–94, 2000) who established a connection between g...

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Bibliographic Details
Published in:Applicable algebra in engineering, communication and computing communication and computing, 2024-11, Vol.35 (6), p.805-820
Main Author: Benkhalifa, Mahmoud
Format: Article
Language:English
Subjects:
Artificial Intelligence
Computer Hardware
Computer Science
Graph theory
Homotopy theory
Original Paper
Polynomials
Symbolic and Algebraic Manipulation
Theory of Computation
Topology
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Summary:An ideal I of Q [ x 1 , ⋯ , x n ] is said to be m -absorbing if any monomial of total degree p > m belongs to I and if there is a monomial M of total degree m such that M ∉ 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 Q [ x 1 , ⋯ , x n ] generated by a family of complete homogeneous symmetric polynomials of the form P rs ( k ) = ∑ t = 1 k x r k - t x s t - 1 , where k ≥ 3 .
ISSN:0938-1279
1432-0622
DOI:10.1007/s00200-022-00591-2