Remarks on $d$-ary partitions and an application to elementary symmetric partitions

Mircea Cimpoeas, Roxana Tanase

We prove new formulas for $p_d(n)$, the number of $d$-ary partitions of $n$, and, also, for its polynomial part. Given a partition $\lambda =({\lambda }_1,\dots ,{\lambda }_{\ell })$, its associated $j$-th…