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  • @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 = {accepted for publication in Journal of Symbolic Computation, 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}
    }