![[Abstract]](http://www.math.ufl.edu/~frank/icons/scroll.gif){kind=icon}
Alexander Berkovich and Frank G. Garvan;
Some Observations on Dyson's New Symmetries of Partitions
Abstract:
We utilize Dyson's concept of the adjoint of a partition to
derive an infinite family of new polynomial analogues of Euler's Pentagonal
Number Theorem.
We streamline Dyson's bijection relating partitions with crank <k
and those with k in the Rank-Set of partitions. Also, we extend
Dyson's adjoint of a partition to MacMahon's ``modular'' partitions
with modulus 2. This way we find a new combinatorial proof of
Gauss's famous identity.
We give a direct combinatorial proof that for n>1 the partitions of n
with crank k are equinumerous with partitions of n with
crank -k.
The url of this page is http://www.math.ufl.edu/~frank/abstracts/dyson.html.
Created by F.G. Garvan
(fgarvan@ufl.edu) on
Wednesday, March 13, 2002.
Last update made Sat Oct 5 12:27:30 EDT 2002.
fgarvan@ufl.edu