A (0, 1) matrix A is strongly unimodular if A is totally unimodular and every matrix obtained from A by setting a nonzero entry to 0 is also totally unimodular. Here we consider the linear discrepancy of strongly unimodular matrices. It was proved by Lováz, et.al.  that for any matrix A, lindisc(A) ≤ herdisc(A). (1) When A is the incidence matrix of a… (More)
In his paper (1942), Ore found necessary and sufficient conditions under which the modular and distributive laws hold in the lattice of equivalence relations on a set S. In the present paper, we consider commuting equivalence relations. It has been proved by J6nsson (1953) that the modular law holds in the lattice of commuting equivalence relations. We give… (More)
Summer 1995. Mentor. Supervised high school students in research.
In this thesis we give a definition of commutativity of Boolean subalgebras which generalizes the notion of commutativity of equivalence relations, and characterize the commutativity of complete Boolean subalgebras by a structure theorem. We study the lattice of commuting Boolean subalgebras of a complete Boolean algebra. We characterize this class of… (More)