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Using elaborate techniques, the author proves some inequalities between ranks of vector partitions [see \textit{F. G. Garvan}, Trans. Am. Math. Soc. 305, No. 1, 47-77 (1988; Zbl 0641.10009); and \textit{M. D. Hirschhorn}, Am. Math. Mon. 97, No. 5, 398-400 (1990; Zbl 0717.11044)].
Partitions; congruences and congruential restrictions, Combinatorial aspects of partitions of integers, Computational Theory and Mathematics, inequalities, \(q\)-calculus and related topics, ranks of vector partitions, Discrete Mathematics and Combinatorics, Combinatorial inequalities, Theoretical Computer Science
Partitions; congruences and congruential restrictions, Combinatorial aspects of partitions of integers, Computational Theory and Mathematics, inequalities, \(q\)-calculus and related topics, ranks of vector partitions, Discrete Mathematics and Combinatorics, Combinatorial inequalities, Theoretical Computer Science
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