MacMahon's Partition Analysis XI: The Search for Modular Forms
Sprache des Titels:
Englisch
Original Kurzfassung:
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
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