DATE: Tuesday, January 26 (2010), at 4:05pm
PLACE: LIT 305
SPEAKER: Krishnaswami Alladi
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TITLE:
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A new look at partitions into distinct odd
parts and connections with Gollnitz's theorem
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ABSTRACT:
The classical result about partitions
of an integer into distinct odd parts is that they
are equal to the number of self conjugate partitions
of that integer. We will give a combinatorial proof of
the following new result: The number of partitions
of n into distinct odd parts equals the number of
partitions of n into parts that differ by ≥ 6,
where the inequality is strict if a part is even, and
2 is not a part. Connections between this result
and Sylvester's refinement of a theorem of Euler
will be discussed. Also, we will indicate how a three
parameter refinement of this is connected to a deep
theorem of Gollnitz.
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