MacMahon's Partition Analysis XI: The Search for Modular Forms

Research output: Working paper and reports › Research report

Abstract

In this paper we continue the partition explorations made possible by Omega, the computer algebra implementation of MacMahon's Partition Analysis. The focus of our work has been partitions associated with directed graphs. The graphs considered here are made up of chains of hexagons, and the related generating functions are infinite products. The culmination of our study leads to an infinite family of modular forms. These, in turen, lead to interesting arithmetic theorems and conjectures for the related partition functions
Original languageEnglish
Number of pages11
Publication statusPublished - 2006

Publication series

NameSFB F013 Reports
No.2006-27

Fields of science

  • 101 Mathematics
  • 101001 Algebra
  • 101005 Computer algebra
  • 101009 Geometry
  • 101012 Combinatorics
  • 101013 Mathematical logic
  • 101020 Technical mathematics

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