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Partition Analysis and its Polyhedral Geometry

Algebra & Discrete Mathematics

Speaker: Zafeirakis Zafeirakopoulos, RISC
Location: 2112 MSB
Start time: Tue, Apr 17 2012, 2:10PM

Partition analysis is a general methodology for the treatment of combinatorial problems subject to linear Diophantine systems.The $\Omega$ operator, introduced by MacMahon 100 years ago, is the central tool of partition analysis. Andrews, Paule and Riese gave a completely algorithmic implementation of the $\Omega$ operator powered by symbolic computation 10 years ago. After an introduction to the partition analysis world, a geometric interpretation of the algorithms implementing partition analysis will be presented. More precisely, the geometry of Elliott reduction and of the fundamental recurrence of Andrews, Paule and Riese. Finally, it will be exhibited how partition analysis relates to some geometric problems.