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BEGIN:VEVENT
UID:d8169917f1b01089a1b5b7e3176b0459
CATEGORIES:Experimental Mathematics Seminar
CREATED:20220925T145439
SUMMARY:Sorting probability for Young diagrams
LOCATION:Zoom
DESCRIPTION:Abstract: Can you always find two elements x,y of a partially ordered set, 
 such that, the probability that x is ordered before y when the poset is ord
 ered randomly, is between 1/3 and 2/3? This is the celebrated 1/3-2/3 Conje
 cture, which has been called "one of the most intriguing problems in the co
 mbinatorial theory of posets". We will explore this conjecture for posets t
 hat arise from (skew-shaped) Young diagrams, where total orderings of these
  posets correspond to standard Young tableaux. We will show that these prob
 abilities are arbitrarily close to 1/2, by using random walk estimates and 
 the state-of-the-art hook-length formulas of Naruse. This is a joint work w
 ith Igor Pak and Greta Panova. This talk is aimed at a general audience.\n
X-ALT-DESC;FMTTYPE=text/html:<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>: Can you always find two elements x,y of
  a partially ordered set, such that, the probability that x is ordered befo
 re y when the poset is ordered randomly, is between 1/3 and 2/3? This is th
 e celebrated 1/3-2/3 Conjecture, which has been called "one of the most int
 riguing problems in the combinatorial theory of posets". We will explore th
 is conjecture for posets that arise from (skew-shaped) Young diagrams, wher
 e total orderings of these posets correspond to standard Young tableaux. We
  will show that these probabilities are arbitrarily close to 1/2, by using 
 random walk estimates and the state-of-the-art hook-length formulas of Naru
 se. This is a joint work with Igor Pak and Greta Panova. This talk is aimed
  at a general audience.</p>
CONTACT:Swee Hong Chan, Rutgers University
X-EXTRAINFO:Zoom Link https://rutgers.zoom.us/j/94346444480 [password: The 20th Catalan
  number, alias (40)!/(20!*21!), alias 6564120420 ]
DTSTAMP:20260827T005741
DTSTART;TZID=America/New_York:20221013T170000
DTEND;TZID=America/New_York:20221013T180000
SEQUENCE:0
TRANSP:OPAQUE
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