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UID:ac8a8df4f3e9172db5b9cd72800f9896
CATEGORIES:Experimental Mathematics Seminar
CREATED:20250908T204151
SUMMARY:Identity Found by Proving Identities
LOCATION:https://rutgers.zoom.us/j/95103383827    password: 6564120420
DESCRIPTION: \nAt the 3rd Formal Power Series and Algebraic Combinatorics conference, t
 hat tool place in Bordeaux in 1991, Doron Zeilberger gave an invited talk w
 ith the title "Identities in Search of Identity". At the same time, his sem
 inal paper on the holonomic systems approach to special function identities
  was published and, together with Herbert Wilf, he developed the WZ theory 
 for proving hypergeometric summation identities. During the following 35 ye
 ars, this theory has been considerably extended and refined, and evolved in
 to its own research area within symbolic computation. We recapitulate its e
 volution, highlight its main achievements, and discuss some recent trends. 
 We then turn our attention to applications in combinatorics, with a special
  emphasis on the treatment of determinants and Pfaffians, which became amen
 able to symbolic methods via the holonomic ansatz: the sought identity may 
 be transformed into a set of summation identities, which themselves can be 
 proven algorithmically. This procedure is elucidated with prominent example
 s, such as the q-enumeration of totally-symmetric plane partitions, the cou
 nting of configurations in the twenty-vertex model, and the evaluation of b
 inomial determinants emerging from rhombus tilings.\n \n
X-ALT-DESC;FMTTYPE=text/html:<p>&nbsp;</p><p style="color: #000000; font-family: 'Times New Roman'; font
 -size: medium; font-weight: 400; letter-spacing: normal; orphans: 2; text-a
 lign: start; text-indent: 0px; text-transform: none; white-space: normal; w
 idows: 2; word-spacing: 0px;">At the 3rd Formal Power Series and Algebraic 
 Combinatorics conference, that tool place in Bordeaux in 1991, Doron Zeilbe
 rger gave an invited talk with the title "Identities in Search of Identity"
 . At the same time, his seminal paper on the holonomic systems approach to 
 special function identities was published and, together with Herbert Wilf, 
 he developed the WZ theory for proving hypergeometric summation identities.
  During the following 35 years, this theory has been considerably extended 
 and refined, and evolved into its own research area within symbolic computa
 tion. We recapitulate its evolution, highlight its main achievements, and d
 iscuss some recent trends. We then turn our attention to applications in co
 mbinatorics, with a special emphasis on the treatment of determinants and P
 faffians, which became amenable to symbolic methods via the holonomic ansat
 z: the sought identity may be transformed into a set of summation identitie
 s, which themselves can be proven algorithmically. This procedure is elucid
 ated with prominent examples, such as the q-enumeration of totally-symmetri
 c plane partitions, the counting of configurations in the twenty-vertex mod
 el, and the evaluation of binomial determinants emerging from rhombus tilin
 gs.</p><p>&nbsp;</p>
CONTACT: Christoph Koutschan, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria
DTSTAMP:20260826T234233
DTSTART;TZID=America/New_York:20251016T170000
DTEND;TZID=America/New_York:20251016T180000
SEQUENCE:0
TRANSP:OPAQUE
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