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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.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20191104-L-Rote.html
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