<div class="csl-bib-body">
<div class="csl-entry">Wallner, M. (2022, May 20). <i>Walks Avoiding a quadrant and the reflection principle</i> [Presentation]. Groupe de travail « Transcendance et Combinatoire », Paris, France. http://hdl.handle.net/20.500.12708/153388</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/153388
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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 phenomenon: 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
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dc.subject
Enumerative combinatorics
en
dc.subject
Enumerative combinatorics
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dc.subject
lattice paths
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dc.subject
non-convex cones
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dc.subject
algebraic series
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dc.title
Walks Avoiding a quadrant and the reflection principle
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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
