We show how to interpret a certain q-series as a generating function for overpartitions with attached parts. A number of families of partition theorems follow as corollaries.

We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set, 3-assignment. For comparing two families of polytopes we use the following method. We say that a family P is affinely reduced to a family Q if for every pol...

In ontology-based data access, data are queried through an ontology that offers a representation of the domain of interest. In this context, correct answers are those entailed by the logical theory constituted by the data and the ontology. Traditional database constraints like tuple-generating dependencies (TGDs) and equality-generating dependencies (EGDs) are a useful tool for ontology specifi...

Schema mappings have been extensively studied in database research over the past decade – notably in the areas of data exchange and data integration. Recently, the notion of an information transfer order on schema mappings has been introduced to compare the amount of source information that is actually transferred by two mappings. In this paper, we present two new operators: the union and inter...

In a recent paper by this author, constructions of linear binary covering codes are considered. In this work, constructions and techniques of the earlier paper are developed and modified for q-ary linear nonbinary covering codes, q 2 3, and new constructions are proposed. The described constructions design an infinite family of codes with covering radius R based on a starting code of the same c...

Many families of pattern-avoiding permutations can be described by a generating tree in which each node carries one integer label, computed recursively via a rewriting rule. A typical example is that of 123-avoiding permutations. The rewriting rule automatically gives a functional equation satisfied by the bivariate generating function that counts the permutations by their length and the label ...

We show that if a Legendrian knot in standard contact R3 possesses a generating family then there exists an augmentation of the Chekanov-Eliashberg DGA so that the associated linearized contact homology is isomorphic to singular homology groups arising from the generating family. We discuss the relationship between normal rulings, augmentations, and generating families. In particular, we provid...

New techniques, both theoretical and practical, are presented for constructing permutation representations for computing with matrix groups defined over finite fields. The permutation representation is constructed on a conjugacy class of subgroups of prime order. We construct a base for the permutation representation, which in turn simplifies the computation of a strong generating set. In addit...

The study and recognition of graph families (or graph properties) is an essential part of combinatorics. Graph colouring is another fundamental concept of graph theory that can be looked at, in large part, as the recognition of a family of graphs that are colourable according to certain rules. In this thesis, we study additive induced-hereditary families, and some generalisations, from a colour...

In this paper, a system for pitch independent musical instrument recognition is presented. A wide set of features covering both spectral and temporal properties of sounds was investigated, and their extraction algorithms were designed. The usefulness of the features was validated using test data that consisted of 1498 samples covering the full pitch ranges of 30 orchestral instruments from the ...