DATES:
Tuesday, February 15 (2011), at 1:55pm
PLACE: LIT 368
SPEAKER:
George Andrews (Penn State)
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TITLE:
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The Anti-Telescoping Method I
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ABSTRACT:
The late Leon Ehrenpreis asked in 1987 whether one could prove
that the number of partitions of n into parts congruent to 1 or 4 mod 5 is
always at least as large as the number of partitions of n into parts
congruent to 2 or 3 mod 5 WITHOUT invoking the Rogers-Ramanujan
identities. In the Erdos Lecture, I outlined the "sort of" solution to
Ehrenpreis's problem given by Baxter and me. I then briefly described the
actual injective solution given by Kadell. Subsequently, Berkovich and
Garvan treated a general class of problems of this nature using
extremely adroitly constructed injections.
In this talk I will illustrate an alternative method
(Anti-Telescoping) which is more analytic and less combinatorial. We
begin with a "toy problem" using this method to show that the number of
partitions on n into odd parts is at least as large as the number of
partitions of n into even parts. The Anti-Telescoping method tells us
that the difference is the number of partitions of n in which each odd is
each even and if one appears it is the unique odd part.
The remainder of the talk is devoted to progressivly harder
problems.
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