Nicolas Smoot,
"A Congruence Family For 2-Elongated Plane Partitions: An Application of the Localization Method"
, in Journal of Number Theory, Vol. 242, Seite(n) 112-153, 1-2023, ISSN: 1096-1658
Original Titel:
A Congruence Family For 2-Elongated Plane Partitions: An Application of the Localization Method
Sprache des Titels:
Englisch
Original Kurzfassung:
George Andrews and Peter Paule have recently conjectured an infinite family of congruences modulo powers of 3 for the 2-elongated plane partition function $d_2(n)$. This congruence family appears difficult to prove by classical methods. We prove a refined form of this conjecture by expressing the associated generating functions as elements of a ring of modular functions isomorphic to a localization of $mathbb{Z}[X]$.
Forschungs-