@

author = {J. Sellers and N. Smoot},}

title = {{On the Divisibility of 7-Elongated Plane Partition Diamonds by Powers of 8}},

language = {english},

abstract = {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.},

number = {22-17},

year = {2022},

month = {February},

keywords = {Partition congruences, infinite congruence family, modular functions, plane partitions, modular curve, Riemann surface},

length = {11},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}