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SUMMARY:George E. Andrews (Pennsylvania State University)
DTSTART:20200602T153000Z
DTEND:20200602T155500Z
DTSTAMP:20260423T011218Z
UID:CANT2020/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/20/
 ">Separable integer partition (SIP) classes</a>\nby George E. Andrews (Pen
 nsylvania State University) as part of Combinatorial and additive number t
 heory (CANT 2021)\n\n\nAbstract\nThree of the most classical and well-know
 n identities in the theory of partitions concern: \n(1) the generating fun
 ction for $p(n)$ (Euler)\; \n(2) the generating function for partitions in
 to distinct parts (Euler)\, and \n(3) the generating function for partitio
 ns in which parts differ by at least 2 (Rogers-Ramanujan).  \nThe lovely\,
  simple argument used to produce the relevant generating functions is most
 ly never seen again.  \nActually\, there is a very general theorem here wh
 ich we shall present.  \nWe then apply it to prove two familiar theorems\;
  (1) G\\" ollnitz-Gordon\, and (2) Schur 1926.  \nWe also consider  an exa
 mple where the series representation for the partitions in question  is ne
 w.  \nWe close with an application to "partitions with n copies of n."\n
LOCATION:https://researchseminars.org/talk/CANT2020/20/
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