A slight variation of Savage and Yee's simpleection for Euler's distinct-odd partition theorem

The $(k,l)$-Euler theorem and the combinatorics of $(k,l)$-sequences

We provide and prove slightvariations of the suggested bijection, not only for the case but also for the cases and with.

Furthermore, we show that our bijections equal the recursive bijections given by bousquet-m\'elou and eriksson in their recursive proof of the hall and finally provide the analogous recursive bijection for the theorem.