<div class="csl-bib-body">
<div class="csl-entry">Wallner, M. (2022, October 14). <i>Walks avoiding a quadrant and the reflection principle</i> [Presentation]. Joint MATHEXP-PolSys Seminar, Inria, Saclay, France. http://hdl.handle.net/20.500.12708/153475</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/153475
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dc.description.abstract
We continue the enumeration of plane lattice walks with small steps avoiding the negative quadrant, initiated by Bousquet-Mélou in 2016. We solve in detail a new case, namely the king model where all eight nearest neighbour steps are allowed. The associated generating function satisfies an algebraicity pheonomeon: it is the sum of a simple, explicit D-finite series (related to the number of walks confined to the first quadrant), and an algebraic one. The principle of the approach is the same as in [Bousquet-Mélou, 2016], but challenging theoretical and computational difficulties arise as we now handle algebraic series of degree up to 216. We expect a similar algebraicity phenomenon to hold for the seven Weyl step sets, which are those for which walks confined to the first quadrant can be counted using the reflection principle. This is now proved for three of them. For the remaining four, we predict the D-finite part of the solution, and in three of the four cases, give evidence for the algebraicity of the remaining part.
en
dc.description.sponsorship
Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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dc.description.sponsorship
Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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dc.language.iso
en
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dc.subject
D-finite series
en
dc.subject
Enumerative combinatorics
en
dc.subject
lattice paths
en
dc.subject
non-convex cones
en
dc.subject
algebraic series
en
dc.title
Walks avoiding a quadrant and the reflection principle
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.relation.grantno
P 34142-N
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dc.relation.grantno
J4162-N35
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dc.type.category
Presentation
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tuw.publication.invited
invited
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tuw.project.title
Gestreckte Exponenten und darüber hinaus
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tuw.project.title
Funktionsgleichungen für Gitter- und Baumstrukturen
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tuw.researchTopic.id
C4
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.value
100
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tuw.linking
https://polsys.lip6.fr/Seminar/seminar.html
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tuw.publication.orgunit
E104-05 - Forschungsbereich Kombinatorik und Algorithmen
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tuw.author.orcid
0000-0001-8581-449X
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tuw.event.name
Joint MATHEXP-PolSys Seminar
en
tuw.event.startdate
14-10-2022
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tuw.event.enddate
14-10-2022
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tuw.event.online
Hybrid
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tuw.event.type
Event for scientific audience
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tuw.event.place
Inria, Saclay
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tuw.event.country
FR
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tuw.event.presenter
Wallner, Michael
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.languageiso639-1
en
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item.openairetype
conference presentation
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item.grantfulltext
none
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item.fulltext
no Fulltext
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item.cerifentitytype
Publications
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item.openairecristype
http://purl.org/coar/resource_type/R60J-J5BD
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crisitem.author.dept
E104 - Institut für Diskrete Mathematik und Geometrie
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crisitem.author.orcid
0000-0001-8581-449X
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crisitem.author.parentorg
E100 - Fakultät für Mathematik und Geoinformation
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crisitem.project.funder
FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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crisitem.project.funder
FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
