3 papers
math.CO2026
A Geometric Characterization of Maximal Unrefinable Partitions via the Keith-Nath Transformation and Young Diagrams
Riccardo Aragona, Roberto Civino, Lorenzo Campioni
We investigate the combinatorial structure of unrefinable partitions through their correspondence with numerical sets and Young diagrams. Building on the bijection introduced by Ke…
math.CO2026
Unrefinable Partitions into Distinct Parts and Numerical Semigroups
Lorenzo Campioni
This article investigates structural connections between unrefinable partitions into distinct parts and numerical semigroups. By analysing the hooksets of Young diagrams associated…
math.CO2025
The number of maximal unrefinable partitions
Riccardo Aragona, Lorenzo Campioni, Roberto Civino
This paper completes the classification of maximal unrefinable partitions, extending a previous work of Aragona et al. devoted only to the case of triangular numbers. We show that…