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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 |
Description
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.