2012/10/26 by John Rhodes, Rhodes, John, Pedro V. Silva +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Topological and Geometric Data Analysis #math.CO #msc:05B20 #msc:05B35 #msc:05E45 #msc:06B15 #msc:15B34
paper · pdf · doi:10.48550/arxiv.1210.7064
57 pages
arxiv created 2012/10/26 · arxiv updated 2012/10/29
Inspired by the work of Izakhian and Rhodes, a theory of representation of hereditary collections by boolean matrices is developed. This corresponds to representation by finite \vee-generated lattices. The lattice of flats, defined for hereditary collections, lattices and matrices, plays a central role in the theory. The representations constitute a lattice and the minimal and strictly join irreducible elements are studied, as well as various closure operators.