Proof of the Andrews-Dyson-Rhoades conjecture on the spt-crank
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Publication:481675
DOI10.1016/j.aim.2014.10.017zbMath1318.11131arXiv1305.2116OpenAlexW1989097353WikidataQ123244015 ScholiaQ123244015MaRDI QIDQ481675
William Y. C. Chen, Wenston J. T. Zang, Kathy Qing Ji
Publication date: 12 December 2014
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1305.2116
Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Analytic theory of partitions (11P82)
Related Items (7)
Asymptotic formulas for spt-crank of partitions ⋮ Inequalities for ranks of partitions and the first moment of ranks and cranks of partitions ⋮ On the non-negativity of the spt-crank for partitions without repeated odd parts ⋮ Asymptotic inequalities for \(k\)-ranks and their cumulation functions ⋮ A REMARK ON TAIL DISTRIBUTIONS OF PARTITION RANK AND CRANK ⋮ Monotonicity properties for ranks of overpartitions ⋮ Unimodality of the Andrews-Garvan-Dyson cranks of partitions
Cites Work
- On the distribution of the \textsf{spt}-crank
- Higher order spt-functions
- Partitions, Durfee symbols, and the Atkin-Garvan moments of ranks
- Relations between the ranks and cranks of partitions
- The odd moments of ranks and cranks
- Mappings and symmetries of partitions
- Some observations on Dyson's new symmetries of partitions
- Combinatorial interpretations of congruences for the spt-function
- Congruences for Andrews’ spt-function modulo powers of $5$, $7$ and $13$
- CRANK 0 PARTITIONS AND THE PARITY OF THE PARTITION FUNCTION
- The number of smallest parts in the partitions of n
- Dyson’s crank of a partition
- Congruences for the Andrews spt function
- Asymptotic inequalities for positive crank and rank moments
- Notes on plane partitions. I
- A new symmetry of partitions
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