Dezső Miklós

On the number of independent functional dependencies

We will investigate the following question: what can be the maximum number of independent functional dependencies in a database of n attributes, that is the maximum cardinality of a system of dependencies which which do not follow from the Armstrong axioms and none of them can be derived from the remaining ones using the Armstrong axioms. An easy and for long time believed to be the best construction is the following: take the maximum possible number of subsets of the attributes such that none of them contains the other one (by the wellknown theorem of Sperner [8] their number is (

On the Security of Individual Data

^{~~n}_{n/2}

On product of association schemes and Shannon capacity

)) and let them all determine all the further values. However, we will show by a specific construction that it is possible to give more than (

Subsums of a Finite Sum and Extremal Sets of Vertices of the Hypercube

^{~~n}_{n/2}

Recent combinatorial results in the theory of relational databases

) independent dependencies (the construction will give (1 +

On fully extended self-avoiding polygons

\frac{1}{n^2}

Combinatorics, Paul Erdős is eighty

) (

Functional dependencies in random databases

^{~~n}_{n/2}

Great intersecting families of edges in hereditary hypergraphs

) of them) and — on the other hand — the upper bound is 2n–1, which is roughly

Diszkrét matematika = Discrete mathematics

\sqrt{n}(^{~~n}_{n/2})