MacMahon's Partition Analysis

EXPERIMENTALl ANALYSIS OF PARTITION COEFFICIENT IN Al-Mg ALLOYS

Because the partition coefficient is one of the most important parameters affecting microsegregation, the aim of this research is to experimentally analyse the partition coefficient in Al-Mg alloys. In order to experimentally measure the partition coefficient, a series of quenching experiments during solidification were carried out. For this purpose binary Al-Mg alloys containing 6.7 and 10.2 w...

Partition Analysis Xii: Plane Partitions

Partition analysis and symmetrizing operators

Using a symmetrizing operator, we give a new expression for the Omega operator used by MacMahon in Partition Analysis, and given a new life by Andrews and his coworkers. Our result is stated in terms of Schur functions. In his book ”Combinatory Analysis”, MacMahon introduced an Omega operator. Recently, Andrews et al [1–3] further developed the theory of Partition Analysis. We show in theorem 4...

PAQ: Partition Analysis of Quasispecies

MOTIVATION The complexities of genetic data may not be accurately described by any single analytical tool. Phylogenetic analysis is often used to study the genetic relationship among different sequences. Evolutionary models and assumptions are invoked to reconstruct trees that describe the phylogenetic relationship among sequences. Genetic databases are rapidly accumulating large amounts of seq...

MacMahon's Partition Analysis: The Omega Package

In his famous book “Combinatory Analysis” MacMahon introduced Partition Analysis (“Omega Calculus”) as a computational method for solving problems in connection with linear homogeneous diophantine inequalities and equations. The object of this paper is to show that partition analysis is ideally suited for being implemented in computer algebra. To this end we have developed the computer algebra ...