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DTSTART;TZID=America/Toronto:20250527T133000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-elise
SUMMARY:Algebraic and enumerative combinatorics seminar-Elise Catania
CLASS:PUBLIC
DESCRIPTION:TITLE:A Toric Analogue for Greene's Rational Function of a Pose
 t \n\nSpeaker\n Elise Catania\n\nAffiliation\n University of Minnesota \n\
 nLocation\n MC 5479\n\nABSTRACT: Given a finite poset\, Greene introduced 
 a rational function\nobtained by summing certain rational functions over t
 he linear\nextensions of the poset. This function has interesting\ninterpr
 etations\, and for certain families of posets\, it simplifies\nsurprisingl
 y. In particular\, Greene evaluated this rational function\nfor strongly p
 lanar posets in his work on the Murnaghan–Nakayama\nformula. Develin\, M
 acauley\, and Reiner introduced toric posets\, which\ncombinatorially are 
 equivalence classes of posets (or rather acyclic\nquivers) under the opera
 tion of flipping maximum elements into minimum\nelements and vice versa. I
 n this work\, we introduce a toric analogue\nof Greene's rational function
  for toric posets\, and study its\nproperties. In addition\, we use toric 
 posets to show that the\nKleiss–Kuijf relations\, which appear in scatte
 ring amplitudes\, are\nequivalent to a specific instance of Greene's evalu
 ation of his\nrational function for strongly planar posets. Also in this w
 ork\, we\ngive an algorithm for finding the set of toric total extensions 
 of a\ntoric poset.
DTSTAMP:20260403T081659Z
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