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DESCRIPTION: We consider paths in the plane governed by the following rules
 : (a) There is a finite set of states. (b) For each state  q \, there is a 
 finite set  S ( q ) of allowable "steps" (( i\,j) \, q ′). This means that 
 from any point ( x \, y ) in state  q \, we can move to ( x + i \, y + j ) 
 in state  q ′. We want to count the number of paths that go from (0\,0) in 
 some starting state q 0  to the point ( n \,0) without ever going below the
   x -axis. There are strong indications that\, under some natural technical
  conditions\, the number of such paths is asymptotic to  C ^  n  /(√ n ^ 3 
 )\, for some "growth constant"  C  which I will show how to compute.   I wi
 ll discuss how lattice paths with states can be used to model asymptotic co
 unting problems for some non-crossing geometric structures (such as trees\,
  matchings\, triangulations) on certain structured point sets. These proble
 ms were recently formulated in terms of so-called production matrices.   Th
 is is ongoing joint work with Andrei Asinowski and Alexander Pilz. 
DTSTAMP:20191118T132100
DTSTART:20191104T141500
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9 
 \n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Günter Rote (Freie Universität Berlin): Lattice paths with states\,
  and counting geometric objects via production matrices
UID:95691492@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/facetsofcomplexity/monday/20191104-L-Rot
 e.html
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