Extending a Recent Result of Santos on Partitions into Odd Parts
نویسنده
چکیده
In a recent note, Santos proved that the number of partitions of n using only odd parts equals the number of partitions of n of the form p1 + p2 + p3 + p4 + . . . such that p1 ≥ p2 ≥ p3 ≥ p4 ≥ · · · ≥ 0 and p1 ≥ 2p2 + p3 + p4 + . . . . Via partition analysis, we extend this result by replacing the last inequality with p1 ≥ k2p2+k3p3+k4p4+. . . , where k2, k3, k4, . . . are nonnegative integers. Several applications of this result are mentioned in closing.
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