Abstract: |
The study of partitions and compositions (i.e., ordered partitions) of
integers goes back centuries and has applications in various areas within
and outside of mathematics. Partition analysis is full of beautiful--and
sometimes surprising--identities, starting with Euler's classic theorem
that the number of partitions of an integer k into odd parts equals the
number of partitions of k into distinct parts.
Motivated by work of George Andrews, Peter Paule, and coauthors from the
last 1 1/2 decades, we will show how one can shed light on certain classes
of partition identities by interpreting partitions as integer points in
polyhedra. Our approach yields both "short" proofs of known results and new
theorems.
This is joint work with Ben Braun, Ira Gessel, Nguyen Le, Sunyoung Lee, and
Carla Savage.
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