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DTSTAMP:20251120T163652Z
DESCRIPTION:Title: Parking functions via piecewise-linear transformations o
 f R^m.\n\nAbstract: Parking functions are certain simple combinatorial obj
 ects which play an important role in the study of symmetric functions. I w
 ill give a very brief indication of their importance\, but my main topic w
 ill be a new characterization of parking functions. A (rational) parking f
 unction can be encoded as a word of length n on the alphabet {0\, ...\, m-
 1}\, but not all words correspond to parking functions. To any word\, we a
 ssociate a piecewise linear transformation of R^m. We show that this trans
 formation has a fixed point if and only if the word corresponds to a parki
 ng function. This is useful because it allows us to prove that a certain m
 ap (usually called 'zeta') from parking functions to parking functions\, d
 efined when m and n are relatively prime\, is in fact a bijection\, verify
 ing a conjecture of Gorsky\, Mazin\, and Vazirani. Perhaps more relevantly
  to the audience\, the geometry of these piecewise-linear transformations 
 seems as if it may also contain further interesting information. This talk
  is based on joint work with Jon McCammond and Nathan Williams.\n
DTSTART:20190213T200000Z
DTEND:20190213T210000Z
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-294451
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