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Binomial Sums and Mellin Asymptotics with Explicit Error Bounds: A Case Study

Authors Benjamin Hackl , Stephan Wagner

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Author Details

Benjamin Hackl
  • Department of Mathematics and Scientific Computing, University of Graz, Austria
Stephan Wagner
  • Institute of Discrete Mathematics, TU Graz, Austria
  • Department of Mathematics, Uppsala University, Sweden

Funding

  • Wagner, Stephan: Supported by the Swedish research council (VR), grant 2022-04030.

Cite AsGet BibTex

Benjamin Hackl and Stephan Wagner. Binomial Sums and Mellin Asymptotics with Explicit Error Bounds: A Case Study. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.AofA.2024.19

Abstract

Making use of a newly developed package in the computer algebra system SageMath, we show how to perform a full asymptotic analysis by means of the Mellin transform with explicit error bounds. As an application of the method, we answer a question of Bóna and DeJonge on 132-avoiding permutations with a unique longest increasing subsequence that can be translated into an inequality for a certain binomial sum.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Generating functions
  • Mathematics of computing → Enumeration
  • Mathematics of computing → Mathematical software
Keywords
  • binomial sum
  • Mellin transform
  • asymptotics
  • explicit error bounds
  • B-terms

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References

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