Six problems of Gian-Carlo Rota in lattice theory and universal algebra
The authors list the most profound mathematical problems investigated by G.-C.\, Rota: 1. Linear lattices (algebraic characterization, free linear lattices, connections to projective geometry, a connection to information theory, Ferrers relations); 2. Lattices and the foundations of probability theory (algebraic and stochastic independence, lattice of commuting \(\sigma \)-subalgebras); 3. Continuous geometries (quantum probability, profinite combinatorics); 4. Expansion of set functions; 5. The generator field of Boolean algebra; 6. Straightening coefficients and Rota's basic conjecture. The list of references includes 37 items of the most significant sources.
scientific article; zbMATH DE number 5163337