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  1. Home > Articles & Issues >
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  3. The Summation Packag ...
Article

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

Carsten Schneider ORCID (1)
(1) Research Institute for Symbolic Computation
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Imported on
March 26, 2015
Published on
January 1, 2004
Last modified on
March 31, 2025
Volume 6
vol. 6:2
DOI
10.46298/dmtcs.313
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https://about.hal.science/hal-authorisation-v1
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The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application

Carsten Schneider ORCID (1)
(1) Research Institute for Symbolic Computation
Abstract
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.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • symbolic summation
  • rhombus tilings
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