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Continuing with the authors concept (and results) of defining independencefor columns of a boolean and superboolean matrix, we apply this theory tofinite lattices and finite posets, introducing boolean and superboolean matrixrepresentations for these objects. These representations yield the new conceptof c-independent subsets of lattices and posets, for which the notion of c-rankis determined as the cardinality of the largest c-independent subset. Wecharacterize this c-rank and show that c-independent subsets have a verynatural interpretation in term of the maximal chains of the Hasse diagram andthe associated partitions of the lattice. This realization has direct importantconnections with chamber systems.

C-independence and c-rank of posets and lattices