Partitions versus sets : a case of duality
Discrete Mathematics
2009-10-20 v2
Abstract
In a recent paper, Amini et al. introduce a general framework to prove duality theorems between special decompositions and their dual combinatorial object. They thus unify all known ad-hoc proofs in one single theorem. While this unification process is definitely good, their main theorem remains quite technical and does not give a real insight of why some decompositions admit dual objects and why others do not. The goal of this paper is both to generalise a little this framework and to give an enlightening simple proof of its central theorem.
Cite
@article{arxiv.0903.2100,
title = {Partitions versus sets : a case of duality},
author = {Laurent Lyaudet and Frédéric Mazoit and Stephan Thomasse},
journal= {arXiv preprint arXiv:0903.2100},
year = {2009}
}