The saturation number for the diamond is linear
Abstract
Abstract For a fixed poset we say that a family is ‐saturated if it does not contain an induced copy of , but whenever we add a new set to , we form an induced copy of . The size of the smallest such family is denoted by . For the diamond poset (the two‐dimensional Boolean lattice), while it is easy to see that the saturation number is at most , the best known lower bound has stayed at since the introduction of the area of poset saturation. In this paper, we prove that , establishing that the saturation number for the diamond is linear. The proof uses a result about certain pairs of set systems.
Fields of Study & Subjects
Algebraic and Geometric Analysis
Polynomial and algebraic computation
Advanced Mathematical Theories and Applications
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 3
- Publication date
- 25 February 2026
- Language
- EN