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SUMMARY:Dennis Davenport (Howard University)
DTSTART:20260915T180000Z
DTEND:20260915T190000Z
DTSTAMP:20260930T020805Z
UID:AI-CoNT/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AI-CoNT/1/">
 Riordan Arrays\, Pseudo-Involutions\, and AI-Assisted Mathematical Discove
 ry</a>\nby Dennis Davenport (Howard University) as part of AI\, Combinator
 ics and Number Theory Seminar\n\n\nAbstract\nThe Riordan group is a group 
 of infinite lower triangular matrices that are defined by\ntwo generating 
 functions\, $g$ and $f$. The $k^{\\mathrm{th}}$ column of each matrix has 
 a generating function related\nto $gf^k$. There are many applications of R
 iordan arrays\, among other things they can be used to\ncount combinatoria
 l objects and to prove combinatorial identities\n\nIn this talk\, I will i
 ntroduce Riordan arrays and discuss recent joint work with Dewayne Dixon a
 nd\nMoussa Doumbia on pseudo-involutions. In the Appell subgroup\, the pse
 udo-involution condition\nreduces to the simple identity\n\\[\ng(z)g(-z)=1
 \,\n\\]\nwhich leads to a useful classification and several interesting in
 teger sequences. I will also discuss\nhow artificial intelligence can assi
 st mathematical discovery by helping generate examples\, identify\npattern
 s\, and suggest conjectures\, while exact computation and proof remain ess
 ential.\n
LOCATION:https://researchseminars.org/talk/AI-CoNT/1/
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