This paper discusses investigations of sequences of natural numbers which count the orbits of an innnite permutation group on n-sets or n-tuples. It surveys known results on the growth rates, cycle index techniques, and an interpretation as the Hilbert series of a graded algebra, with a possible application to the question of smoothness of growth. I suggest that these orbit-counting sequences a...

Clique Generalizations and Related Problems

Locality is a peculiarity which is exhibited by many problems appearing in the most disparate domains of theoretical computer science and mathematics. In this thesis, we demonstrate this assertion by studying three classes of problems that are related to the task of communicating, computing and exploring, respectively. By a local problem, we understand a problem which is easily solved if the pr...

A simple algorithm to calculate the maximum torsional load for a cylindrical shaft is presented. The algorithm is based on the notion of viscosity solutions to the eikonal equation, and is not restricted to simply-connected cross-sections. Applications to other, related problems, such as ferromagnetic thin lms, and elastic buckling of thin lm blisters are also discussed. 1. Introduction A class...

The problem of deciding whether a monoid that is given through a nite presentation is a regular monoid as well as two closely related decision problems are considered. Since these problems are undecidable in general, they are investigated for certain restricted classes of nite presentations. Some new decidability results as well as some new undecidability results are obtained, which show that f...

BACKGROUND Drug-related problems are prevalent and cause considerable patient morbidity and in some cases death, as well as increased health care expenditures. A classification system may contribute to identify such problems, and further to resolve and prevent them. MATERIAL AND METHODS A draft classification was circulated to a panel of physicians and pharmacists and comments were requested....

Alberto Marchetti-Spaccamela University of Rome “La Sapienza” 40.

For an /-uniform hypergraph 3and an integer n, the Turan number ex(n, F) for F on n vertices is denned to be the maximum size \Q\ of a hypergraph Q C [n] not containing a copy of F C2\ as a subhypergraph. For 1 = 1 and f = Kk , the complete graph on k vertices, these numbers were determined by P. Turan. However, for I > 2, and nearly any hypergraph F, the Turan problem of determining the number...

Knapsack problems and variants thereof arise in several different fields from operations research to cryptography to really, really serious problems for hard−core puzzle enthusiasts. We discuss some of these and show ways in which one might formulate and solve them using Mathematica.