Discrete Mathematics ( IF 0.770 ) Pub Date : 2020-01-10 , DOI: 10.1016/j.disc.2019.111805
Runqiao Li; Andrew Y.Z. Wang

Recently, Beck posed two conjectures on the difference between the number of (respectively, distinct) parts in the odd partitions of $n$ and the number of (respectively, distinct) parts in the distinct partitions of $n$. These two conjectures were first confirmed by Andrews using generating functions, and then generalized by Fu and Tang, and Yang in different ways. Motivated by Yang’s work, we present two more generalized results and prove them both analytically and combinatorially.

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