Partitions of a finite Boolean lattice into intervals

Authors:
Josep M. Brunat;António Guedes de Oliveira;Marc Noy
Affiliations:
Departament de Matemítica Aplicada II, Universitat Politécnica de Catalunya, Spain;CMUP and Departamento de Matemática Pura, Universidade do Porto, Portugal;Departament de Matemítica Aplicada II, Universitat Politécnica de Catalunya, Spain
Venue:
European Journal of Combinatorics
Year:
2009

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Abstract

Related to activities in matroids, J.E. Dawson introduced a construction that leads to partitions of the Boolean lattice of parts of a set into intervals. In this paper we characterize explicitly the partitions of a Boolean lattice into intervals that arise from this construction, and we prove that the construction is essentially unique.