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  1. Home > Articles & Issues >
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Conference paper

Algorithmic and combinatoric aspects of multiple harmonic sums

Christian Costermans (1), Jean-Yves Enjalbert (1), Hoang Ngoc Minh (1)
(1) Université de Lille, Sciences et Technologies
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May 10, 2017
Published on
December 31, 2004
Last modified on
March 31, 2025
Volume 0
DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms
Proceedings
DOI
10.46298/dmtcs.3369
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https://about.hal.science/hal-authorisation-v1
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Algorithmic and combinatoric aspects of multiple harmonic sums

Christian Costermans (1), Jean-Yves Enjalbert (1), Hoang Ngoc Minh (1)
(1) Université de Lille, Sciences et Technologies
Abstract
Ordinary generating series of multiple harmonic sums admit a full singular expansion in the basis of functions $\{(1-z)^α \log^β (1-z)\}_{α ∈ℤ, β ∈ℕ}$, near the singularity $z=1$. A constructive proof of this result is given, and, by combinatoric aspects, an explicit evaluation of Taylor coefficients of functions in some polylogarithmic algebra is obtained. In particular, the asymptotic expansion of multiple harmonic sums is easily deduced.
Keywords
  • [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]
  • [INFO.INFO-HC]Computer Science [cs]/Human-Computer Interaction [cs.HC]
  • Lyndon words
  • shuffle algebra
  • polylogarithms
  • polyzêtas
  • multiple harmonic sums
  • singular expansion
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