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UID:21eff3bc7d25e8ef209929181935a5ff
CATEGORIES:Experimental Mathematics Seminar
CREATED:20241010T183701
SUMMARY:q-Factorization of power series
LOCATION:https://rutgers.zoom.us/j/91865817691  [password: The 20th Catalan number\,
  alias (40)!/(20!*21!)\, alias 6564120420 ]
DESCRIPTION:<p><em style="color: #000000; font-family: 'Times New Roman'; font-size: me
 dium; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: sta
 rt; text-indent: 0px; text-transform: none; white-space: normal; widows: 2;
  word-spacing: 0px;">Abstract</em>: In The Theory of Partitions, p. 98, Ex.
  2, George Andrews points out that any power series with constant term 1 ha
 s a unique factorization in the form 1 + r(1)*q + r(2)*q^2 + r(3)*q^3 + . .
  . = (1-q)^{-a_1} * (1-q^2)^{-a_2} * (1-q^3)^{-a^3} * . . . . He then sugge
 sts an algorithm to calculate the r(n) given the a_i . In his qseries.m Map
 le package, Frank Garvan programmed the inverse algorithm, i.e. given the r
 (n), find the a_i. Shashank Kanade and Matthew Russell used this algorithm 
 extensively in their discovery of many new Rogers--Ramanujan type identitie
 s, where the a_i form a discrete periodic function with respect to a fixed 
 modulus. In 1954, G. Meinardus published an asymptotic formula for the r(n)
  in terms of the a_i. Recently, I found an exact formula for the r(n) in te
 rms of the a_i and vice versa, which I will share after presenting some bac
 kground material. This work is part of a larger ongoing project joint with 
 Robert Schneider and Hunter Waldron of Michigan Tech.</p>
CONTACT:Andrew Sills, Georgia Southern University
DTSTAMP:20260828T123519
DTSTART;TZID=America/New_York:20241107T170000
DTEND;TZID=America/New_York:20241107T180000
SEQUENCE:0
TRANSP:OPAQUE
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