Carsten Schneider - The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application

dmtcs:313 - Discrete Mathematics & Theoretical Computer Science, January 1, 2004, Vol. 6 no. 2 - https://doi.org/10.46298/dmtcs.313
The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application

Authors: Carsten Schneider ORCID-iD

    We give an overview of how a huge class of multisum identities can be proven and discovered with the summation package Sigma implemented in the computer algebra system Mathematica. General principles of symbolic summation are discussed. We illustrate the usage of Sigma by showing how one can find and prove a multisum identity that arose in the enumeration of rhombus tilings of a symmetric hexagon. Whereas this identity has been derived alternatively with the help of highly involved transformations of special functions, our tools enable to find and prove this identity completely automatically with the computer.


    Volume: Vol. 6 no. 2
    Published on: January 1, 2004
    Imported on: March 26, 2015
    Keywords: symbolic summation,rhombus tilings,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
    Fundings :
      Source : OpenAIRE Research Graph
    • Symbolic Summation in Difference Fields; Funder: Austrian Science Fund (FWF); Code: P 16613

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