The Structure of Submodular Separation Systems
Christian Elbracht, Jay Lilian Kneip, Maximilian Teegen
TL;DR
This paper explores the structural and order-theoretic properties of abstract separation systems and partial lattices, examining how different submodularity conditions influence their relationships and characteristics.
Contribution
It provides a detailed analysis of the structural and submodularity aspects of separation systems and partial lattices, clarifying their interrelations.
Findings
Different submodularity conditions have distinct impacts on separation systems.
Structural properties of partial lattices are characterized in relation to separation systems.
The relationships between various submodularity conditions are systematically analyzed.
Abstract
We analyse various structural and order-theoretical aspects of abstract separation systems and partial lattices, as well as the relationship between the different submodularity conditions one can impose on them.
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Taxonomy
TopicsAdvanced Algebra and Logic · semigroups and automata theory · Fuzzy and Soft Set Theory