Partitions versus sets: A case of duality

In a recent paper, Amini et al. introduced a general framework to prove duality theorems between tree decompositions and their dual combinatorial object. They unify all known ad-hoc proofs in one duality theorem based on submodular partition functions. This general theorem remains however a bit technical and relies on this particular submodularity property. Instead of partition functions, we propose here a simple combinatorial property of set of partitions which also gives these duality results. Our approach is both simpler, and a little bit more general.

• Type: Journal
• Year: 2010
• Where: EJC
• Authors: Laurent Lyaudet, Frédéric Mazoit, Stéphan Thomassé
• Keywords: Dual Combinatorial Object, EJC 2007, EJC 2010, Partition Functions, Submodular Partition Functions