Koustav Banerjee, Nicolas Smoot,
"The localization method applied to k-elognated plane partitions and divisibily by 5"
, Serie RISC Report Series, Johannes Kepler University Linz, Nummer 22-21, RISC, JKU, Hagenberg, Linz, 8-2022, ISSN: 2791-4267
The localization method applied to k-elognated plane partitions and divisibily by 5
Sprache des Titels:
The enumeration $d_k(n)$ of k-elongated plane partition diamonds has emerged as a generalization of the classical integer partition function p(n). We have discovered an infinite congruence family for $d_5(n)$ modulo powers of 5. Classical methods cannot be used to prove this family of congruences. Indeed, the proof employs the recently developed localization method, and utilizes a striking internal algebraic structure which has not yet been seen in the proof of any congruence family. We believe that this discovery poses important implications on future work in partition congruences.
Sprache der Kurzfassung:
RISC Report Series, Johannes Kepler University Linz