5 papers
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…
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…
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…
Verification and generation of unrefinable partitions
Riccardo Aragona, Lorenzo Campioni, Roberto Civino +1
Unrefinable partitions are a subset of partitions into distinct parts which satisfy an additional unrefinability property. More precisely, being an unrefinable partition means that…
On the maximal part in unrefinable partitions of triangular numbers
Riccardo Aragona, Lorenzo Campioni, Roberto Civino +1
A partition into distinct parts is refinable if one of its parts can be replaced by two different integers which do not belong to the partition and whose sum is , and it is…