Constructing Q -Ideals for Boolean Semiring Partitioning Using Seeds

Claudia Ledbury Justus (), Karin-Therese Howell and Cang Hui
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Claudia Ledbury Justus: Department of Mathematics, Stellenbosch University, Stellenbosch 7602, South Africa
Karin-Therese Howell: Department of Mathematics, Stellenbosch University, Stellenbosch 7602, South Africa
Cang Hui: Department of Mathematics, Stellenbosch University, Stellenbosch 7602, South Africa

Mathematics, 2025, vol. 13, issue 8, 1-20

Abstract: Semiring partitioning is widely used in mathematics, computer science, and data analysis. The purpose of this paper is to add to the theory of semirings by proposing a novel method to construct Q -ideals for partitioning Boolean semirings. We introduce the set of all seeds—all s -tuples over a particular Boolean algebra—and the notion of their weight and complement. Utilizing this new method for constructing Q -ideals, we develop a nested hierarchical partitioning algorithm based on the weight of selected seeds. Additionally, we determine the maximal semiring homomorphism corresponding to this proposed method.

Keywords: semirings; partitioning ideals; ideals; site-by-species matrices (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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