Mathematical analysis demonstrates that log-concavity implies the Bessenrodt–Ono inequality for partition sequences, resolving key aspects of conjectures on l-ary partitions.
We consider infinite sequences of positive numbers. The connection between log-concavity and the Bessenrodt–Ono inequality has been the focus of several papers. It has applications in the white noise distribution theory and combinatorics. We improve a recent result by Benfield and Roy and show that for the sequence of partition numbers (n)\ { p ( n ) } , Nicolas’ log-concavity result implies the result by Bessenrodt and Ono towards $$p(n) \, p(m) > p(n+m)$$ p ( n ) p ( m ) > p ( n + m ) . We provide several examples. Benfield and Roy gave a conjecture related to ℓ -ary partition numbers. We prove a part of this conjecture.
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Heim et al. (2026) studied this question.
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