Wallner, M. (2022). On the critical exponents of generalized ballot sequences in three dimensions and large tandem walks. Aequationes Mathematicae, 96(4), 815–826. https://doi.org/10.1007/s00010-022-00876-4
E104-05 - Forschungsbereich Kombinatorik und Algorithmen
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Journal:
Aequationes Mathematicae
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ISSN:
0001-9054
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Date (published):
Aug-2022
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Number of Pages:
12
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Publisher:
SPRINGER BASEL AG
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Peer reviewed:
Yes
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Keywords:
Bijection; D-finite; Dyck paths; Non-D-finite; Walks in the quarter plane
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Abstract:
We answer some questions on the asymptotics of ballot walks raised in [S. B. Ekhad and D. Zeilberger, April 2021] and prove that these models are not D-finite. This short note demonstrates how the powerful tools developed in the last decades on lattice paths in convex cones help us to answer some challenging problems that were out of reach for a long time. On the way we generalize tandem walks to the family of large tandem walks whose steps are of arbitrary length and map them bijectively to a generalization of ballot walks in three dimensions.
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Project title:
Gestreckte Exponenten und darüber hinaus: P 34142-N (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
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Research Areas:
Computer Science Foundations: 10% Fundamental Mathematics Research: 90%
