2011/10/17 by Zur Izhakian, Izhakian, Zur, John Rhodes +1
Computer Science · Mathematics · #03G05 #05B35 #06G75 #52B40 #55U10 #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Metric Geometry (math.MG) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1110.3553
openalex publication_date 2011/10/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31
Continuing with the authors concept (and results) of defining independence for columns of a boolean and superboolean matrix, we apply this theory to finite lattices and finite posets, introducing boolean and superboolean matrix representations for these objects. These representations yield the new concept of c-independent subsets of lattices and posets, for which the notion of c-rank is determined as the cardinality of the largest c-independent subset. We characterize this c-rank and show that c-independent subsets have a very natural interpretation in term of the maximal chains of the Hasse diagram and the associated partitions of the lattice. This realization has direct important connections with chamber systems.