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- W3023028295 abstract "In this paper, we show that the difference between the number of parts in the odd partitions of $n$ and the number of parts in the distinct partitions of $n$ satisfies Euler's recurrence relation for the partition function $p(n)$ when $n$ is odd. A decomposition of this difference in terms of the total number of parts in all the partitions of $n$ is also derived. In this context, we conjecture that for $k>0$, the series $$ (q^2;q^2)_infty sum_{n=k}^infty frac{q^{{kchoose 2}+(k+1)n}}{(q;q)_n} begin{bmatrix} n-1k-1 end{bmatrix} $$ has non-negative coefficients." @default.
- W3023028295 created "2020-05-13" @default.
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- W3023028295 date "2020-05-07" @default.
- W3023028295 modified "2023-09-27" @default.
- W3023028295 title "On the partitions into distinct parts and odd parts." @default.
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