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We study maximal families A of subsets of [n] = {1, 2,. .. , n} such that A contains only pairs and triples and A ⊆ B for all {A, B} ⊆ A, i.e. A is an antichain. For any n, all such families A of minimum size are determined. This is equivalent to finding all graphs G = (V, E) with |V | = n and with the property that every edge is contained in some triangle… (More)

Keys allow a database management system to uniquely identify tuples in a database. Consequently, the class of keys is of great significance for almost all data processing tasks. In the relational model of data, keys have received considerable interest and are well understood. However, for efficient means of data processing most commercial relational… (More)

We consider the poset of all submatrices of a given matrix, ordered by containment. The unique rank function for this poset is given by r(M) = R(M)+C(M)?1, where R(M) and C(M) denote the number of rows and columns of a nonempty matrix M, respectively, and the rank of the empty matrix is 0. For xed k and i our objective is to nd a set M of submatrices M 1 ;… (More)

Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Abstract. Possibility theory is applied to introduce and reason about the fundamental notion of a key for uncertain data. Uncertainty is modeled… (More)

We discuss the existence of matrix representations for gener-alised and minimum participation constraints which are frequently used in database design and conceptual modelling. Matrix representations, also known as Armstrong relations, have been studied in literature e.g. for functional dependencies and play an important role in example-based design and for… (More)

We consider the poset SO(n) of all words over an n{element alphabet ordered by the subword relation. It is known that SO(2) falls into the class of Macaulay posets, i.e. there is a theorem of Kruskal{Katona type for SO(2). As the corresponding linear ordering of the elements of SO(2) the vip{order can be chosen. Daykin introduced the V {order which… (More)