@**techreport**{RISC5338,author = {Ralf Hemmecke},

title = {{Dancing Samba with Ramanujan Partition Congruences}},

language = {english},

abstract = {The article presents an algorithm to compute a $C[t]$-module basis
$G$ for a given subalgebra $A$ over a polynomial ring $R=C[x]$ with
a Euclidean domain $C$ as the domain of coefficients and $t$ a given
element of $A$.
The reduction modulo $G$ allows a subalgebra membership test.
The algorithm also works for more general rings $R$, in particular
for a ring $R\subset C((q))$ with the property that $f\in R$ is zero
if and only if the order of $f$ is positive.
As an application, we algorithmically derive an explicit identity
(in terms of quotients of Dedekind $\eta$-functions and Klein's
$j$-invariant) that shows that $p(11n+6)$ is divisible by 11 for
every natural number $n$ where $p(n)$ denotes the number of
partitions of $n$.
},

number = {16-06},

year = {2016},

month = {jun},

note = {Journal of Symbolic Computation 84, 2018, http://dx.doi.org/10.1016/j.jsc.2017.02.001},

keywords = {partition identities \sep number theoretic algorithm \sep subalgebra basis},

length = {14},

type = {RISC Report Series},

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

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}