@

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 $n$. },

journal = {Journal of Symbolic Compuation},

volume = {84},

pages = {14--24},

isbn_issn = {0747-7171},

year = {2018},

note = {Also available as RISC Report 16-06 https://www.risc.jku.at/publications/download/risc_5338/DancingSambaRamanujan.pdf},

refereed = {yes},

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

length = {11},

url = {http://dx.doi.org/10.1016/j.jsc.2017.02.001}