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UID:6909@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20191121T110000
DTEND;TZID=Europe/Paris:20191121T123000
DTSTAMP:20241120T202623Z
URL:https://www.i2m.univ-amu.fr/evenements/luigi-santocanale-on-discrete-i
 dempotent-paths/
SUMMARY:Luigi Santocanale (LIS\, LIRICA team\, Aix-Marseille Université): 
 On discrete idempotent paths
DESCRIPTION:Luigi Santocanale: The set of discrete lattice paths from (0\, 
 0) to (n\, n) with North and East steps (i.e. words w ∈ { x\, y } * such
  that |w| x = |w| y = n) has a canonical monoid structure inherited from t
 he bijection with the set of join-continuous maps from the chain { 0\, 1\,
 . .. \, n } to itself. We explicitly describe this monoid structure and\, 
 relying on a general characterization of idempotent join-continuous maps f
 rom a complete lattice to itself\, we characterize idempotent paths as upp
 er zigzag paths. We argue that these paths are counted by the odd Fibonacc
 i numbers. Our method yields a geometric/combinatorial proof of counting r
 esults\, due to Howie and to Laradji and Umar\, for idempotents in monoids
  of monotone endomaps on finite chains.\n\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Luigi_Santocanale.jpg
CATEGORIES:Séminaire,Logique et Interactions
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DTSTART:20191027T020000
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