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UID:20260620T054849EDT-0265Js7dSc@132.216.98.100
DTSTAMP:20260620T094849Z
DESCRIPTION:Title: Parking functions via piecewise-linear transformations o
 f Rm\n\nAbstract: Parking functions are certain simple combinatorial objec
 ts which play an important role in the study of symmetric functions. I wil
 l give a very brief indication of their importance\, but my main topic wil
 l be a new characterization of parking functions. A (rational) parking fun
 ction can be encoded as a word of length n on the alphabet {0\,…\,m−1}\, b
 ut not all words correspond to parking functions. To any word\, we associa
 te a piecewise linear transformation of Rm. We show that this transformati
 on has a fixed point if and only if the word corresponds to a parking func
 tion. This is useful because it allows us to prove that a certain map (usu
 ally called 'zeta') from parking functions to parking functions\, defined 
 when m and n are relatively prime\, is in fact a bijection\, verifying a c
 onjecture of Gorsky\, Mazin\, and Vazirani. Perhaps more relevantly to the
  audience\, the geometry of these piecewise-linear transformations seems a
 s if it may also contain further interesting information. This talk is bas
 ed on joint work with Jon McCammond and Nathan Williams.\n\n \n
DTSTART:20190220T200000Z
DTEND:20190220T210000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Hugh Thomas (UQAM)
URL:/mathstat/channels/event/hugh-thomas-uqam-294761
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