The Omega Transform and Generating Functions -- Mohammad Moinul Haque, February 15, 2005

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The Omega Transform is a powerful tool from Partition 
Analysis.  First developed by Major Percy MacMahon in the early 
20th century to solve problems in partition theory by computing 
their generating functions, understanding and making use of this  
transform has in fact become a somewhat current field of 
research in this part of mathematics.  I will discuss what this
transform is and give examples of where it is useful.  In 
particular, in the last part of the talk I will discuss how I 
used this tool to solve combinatorial problems arising from 
arithmetic algebraic geometry as part of Prof. Glass' group in 
the Columbia Summer Research Program.

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