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BEGIN:VEVENT
UID:2a46113e0f677838157bad518dd05c81
CATEGORIES:Experimental Mathematics Seminar
CREATED:20210125T135902
SUMMARY:Cyclic permutations, shuffles, and quasi-symmetric functions
LOCATION:zoom
DESCRIPTION:<p><span style="font-family: Times New Roman; font-size: medium;"> <span st
 yle="font-family: Times New Roman;"><i><span style="color: black; font-size
 : 13.5pt;">Abstract</span></i><span style="color: black; font-size: 13.5pt;
 ">: Richard Stanley proved that the distribution of descent number over all
  the shuffles of two permutations depends only on the descent numbers of th
 e permutations.</span></span></span></p><p><span style="font-family: Times 
 New Roman; font-size: medium;"> <span style="color: black; font-size: 13.5p
 t;"><span style="font-family: Times New Roman;">We present an explicit cycl
 ic analogue of this result. The tools used for the proof include a new cycl
 ic counterpart of Gessels quasi-symmetric functions, an unusual ring homomo
 rphism, and a mysterious binomial identity with an interesting history.</sp
 an></span></span></p><p><span style="font-family: Times New Roman; font-siz
 e: medium;"> <span style="color: black; font-size: 13.5pt;"><span style="fo
 nt-family: Times New Roman;">Based on joint work with Ira Gessel, Vic Reine
 r, and Yuval Roichman.</span></span></span></p><p><span style="font-family:
  Times New Roman; font-size: medium;"> </span></p>
CONTACT: Ron Adin, Bar Ilan University
X-EXTRAINFO:https://rutgers.zoom.us/j/94346444480#success\npassword: The 20th Catalan n
 umber, alias (40)!/(20!*21!), alias 6564120420 
DTSTAMP:20260920T203701
DTSTART;TZID=America/New_York:20210204T170000
DTEND;TZID=America/New_York:20210204T180000
SEQUENCE:0
TRANSP:OPAQUE
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