James Sellers, Nicolas Smoot,
"On the Divisibility of 7-Elongated Plane Partition Diamonds by Powers of 8"
, Serie RISC Report Series, Johannes Kepler University Linz, Austria, Nummer 22-17, RISC, JKU, Hagenberg, Linz, 2022, ISBN: 2791-4267
Original Titel:
On the Divisibility of 7-Elongated Plane Partition Diamonds by Powers of 8
Sprache des Titels:
Englisch
Original Kurzfassung:
In 2021 da Silva, Hirschhorn, and Sellers studied a wide variety of congruences for the $k$-elongated plane partition function $d_k(n)$ by various primes. They also conjectured the existence of an infinite congruence family modulo arbitrarily high powers of 2 for the function $d_7(n)$. We prove that such a congruence family exists---indeed, for powers of 8. The proof utilizes only classical methods, i.e., integer polynomial manipulations in a single function, in contrast to all other known infinite congruence families for $d_k(n)$ which require more modern methods to prove.
Sprache der Kurzfassung:
Englisch
Veröffentlicher:
RISC, JKU
Verlagsanschrift:
Hagenberg, Linz
Serie:
RISC Report Series, Johannes Kepler University Linz, Austria
Forschungs-