Eecient Generation of Graphical Partitions

Graphical Basis Partitions

A partition of an integer n is graphical if it is the degree sequence of a simple undirected graph It is an open question whether the fraction of partitions of n which are graphical approaches as n approaches in nity A partition is basic if the number of dots in its Ferrers graph is minimum among all partitions with the same rank vector as In this paper we investigate graphical partitions via b...

On the Number of Graphical Forest Partitions

A graphical partition of the even integer n is a partition of n where each part of the partition is the degree of a vertex in a simple graph and the degree sum of the graph is n. In this note, we consider the problem of enumerating a subset of these partitions, known as graphical forest partitions, graphical partitions whose parts are the degrees of the vertices of forests (disjoint unions of t...

Dominance Order and Graphical Partitions

We gave a new criterion for graphical partitions. We derive a new recursion formula, which allows the computation of the number g(n) of graphical partitions of weight n for up to n > 900.

Eecient Speciication-based Oracles for Critical Systems

EEective testing of critical systems has been hampered by the lack of a cost-eeective method for deciding the correctness of a program's behavior under test. Using formal speciications to describe the critical system properties and then checking test results against these spe-ciications overcomes these problems. If these test oracles , which are mechanisms for determining whether a test passes ...

Eecient Discovery of Functional and Approximate Dependencies Using Partitions (extended Version)