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DESCRIPTION: A directed lattice path is a polygonal line which starts at th
e origin and consists of several vectors of the form (1\, y) (where y belon
gs to a fixed set of integers) appended to each other. Enumeration of diffe
rent kinds of lattice paths (walks/bridges/meanders/excursions) was accompl
ished by Banderier and Flajolet in 2002. We refine and generalize their res
ults by studying lattice paths that avoid a fixed pattern (or several patte
rns). To this end\, we develop a "vectorial kernel method" – a unified fram
ework for enumeration of words generated by a counter automaton. Another im
protant tool is the "autocorrelation polynomial" that encodes self-overlapp
ings of a pattern\, and its generalization: the "mutual correlation matrix"
for several patterns. (This talk is based on joint works with Cyril Bander
ier\, Axel Bacher\, Bernhard Gittenberger and Valerie Rointer.)
DTSTAMP:20191129T150100
DTSTART:20200113T160000
CLASS:PUBLIC
LOCATION:Technische Universität Berlin\n Institut für Mathematik\n Straße d
es 17. Juni 136\n 10623 Berlin\n Room MA 041 (Ground Floor)
SEQUENCE:0
SUMMARY:Andrei Asinowski (Universität Klagenfurt): Vectorial kernel method
and patterns in lattice paths
UID:95692881@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20200113-C-Asinowski.html
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