2025/04/07 by Dale Worley, Worley, Dale R.
Computer Science · Engineering · #06B15 #Advanced Materials and Mechanics #Combinatorics (math.CO) #FOS: Mathematics #Logic, programming, and type systems #Music Technology and Sound Studies
paper · pdf · doi:10.48550/arxiv.2504.05507
openalex publication_date 2025/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper explores alternative statements of the axioms for lattice gluing, focusing on lattices that are modular, locally finite, and have finite covers, but may have infinite height. We give a set of "maximal" axioms that maximize what can be immediately adduced about the structure of a valid gluing. We also give a set of "minimal" axioms that minimize what needs to be adduced to prove that a system of blocks is a valid gluing. This system appears to be novel in the literature. A distinctive feature of the minimal axioms is that they involve only relationships between elements of the skeleton which are within an interval [x \wedge y, x \vee y] where either x and y cover x \wedge y or they are covered by x \vee y. That is, they have a decidedly local scope, despite that the resulting sum lattice, being modular, has global structure, such as the diamond isomorphism theorem.