FWF Logo National Research Network S9600
Analytic Combinatorics and Probabilistic Number Theory


Project S9611 - The Hardy-Littlewood method in the analysis of digit problems and enumerative combinatorics

Principal Investigator

Robert F. Tichy

Co-Investigator

Jörg Thuswaldner

Funded Researchers

Manfred Madritsch

Description

This research project combines the two main subjects of the network insofar as it deals with combinatoric as well as number-theoric questions and has thus many relations to other projects of the NFN. The link between combinatorics and number theory is given by the common use of analytical methods for enumeration, in particular, the Hardy-Littlewood circle method and related techniques. These techniques build a remarkable connection between such different subjects as number theory and theoretical chemistry.

One main point of our research program will be the study of digitally restricted sets; for instance, the set of integers with fixed q-adic sum of digits or missing digits in the q-adic expansion will be of interest. In particular, we want to study problems of the Waring-Goldbach type for these sets by means of the Hardy-Littlewood method and related analytic methods.

On the other hand, the combinatorics of graph-theoretical indices will be the second main point of investigation in this subproject. It is known that some graph characteristics, such as the Wiener index (sum of all distances) or the Merrifield-Simmons index (number of independent vertex subsets) reflect the physicochemical properties of molecules quite well. Corresponding questions like the inverse problem (given an index, construct a graph with this index) or average problems lead to interesting number-theoretic and combinatoric investigations.