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UID:8a5bdfd944aad70d9464581b809be60a
CATEGORIES:Experimental Mathematics Seminar
CREATED:20250417T193440
SUMMARY:Spanning Trees ; Permutation Wordle
LOCATION:https://rutgers.zoom.us/j/94346444480 [password: The 20th Catalan number\, 
 alias (40)!/(20!*21!)
DESCRIPTION:<p>First Talk:Generating functions of sequences relating to spanning trees 
 in certain graph families Abstract: Kirchhoff's Matrix Tree Theorem allows 
 us to compute the number of spanning trees of a graph by looking at its Lap
 lacian matrix. For certain graph families (in our case, powers of cycles an
 d paths), which are represented by finitely many states, we know by the Tra
 nsfer Matrix Method that a rational generating function exists for sequence
 s arising from structures in the family. Such a generating function can be 
 found by computing sufficiently many terms of the sequence. In joint work w
 ith Doron Zeilberger, we found generating functions for the number of spann
 ing trees and for a leaf-parameter by experimental methods.</p><p>Second Ta
 lk:Consider a game of permutation wordle in which a player attempts to gues
 s a secret permutation in Sn in as few guesses as possible. In each round, 
 the guessing player is told which indices of their guessed permutation are 
 correct. How can we optimize the player's strategy? Samuel Kutin and Lawren
  Smithline propose a strategy called cyclic shift in which all incorrect en
 tries are shifted one index to the right in successive guesses, and they co
 njecture its optimality. We investigate this conjecture by formalizing what
  a "strategy" looks like, performing experimental analysis on inductively c
 onstructed strategies, and taking advantage of Kutin-Smithline's findings r
 elated to Eulerian numbers.</p><p>&nbsp;</p><p>&nbsp;</p>
CONTACT: Pablo Blanco  (first talk),  Aurora Hiveley (second talk)
DTSTAMP:20260828T185000
DTSTART;TZID=America/New_York:20250501T170000
DTEND;TZID=America/New_York:20250501T180000
SEQUENCE:0
TRANSP:OPAQUE
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