Generalized Rogers-Ramanujan bijections
In an earlier paper [Discrete Math. 38, 313--315 (1982; Zbl 0476.05010)] the authors presented a short combinatorial proof of the first Rogers-Ramanujan identity, which states that the partitions of \(n\) into parts differing by at least two are equinumerous with the partitions of \(n\) with all parts \(\equiv\pm 1\pmod 5\). In the present paper they explain how the relevant bijection was obtained, and further give a much more general bijection closely related to results of \textit{D. M. Bressoud} [J. Number Theory 16, 235--241 (1983; Zbl 0516.10008)]. Among consequences of these results is the following: for given \(n,k\), the partitions of \(n\) with no part \(\equiv 0\) or \(\pm k\pmod{2k+1}\) are equinumerious with the partitions of \(n\) with no parts below the \((k-1)\)th Durfee square.
scientific article; zbMATH DE number 4122000