Liu's conjecture on gap-level excedance and Denert statistics
Let and , and let and denote the -gap -level excedance number and -gap -level Denert statistic, respectively. Set . A pair of permutation statistics is -Euler-Mahonian when its bivariate distribution over agrees with that of . Liu's conjecture. For all and , the pair is -Euler-Mahonian, where . The paper's abstract says that its main objective is to confirm this conjecture, and the supplied proof passage says that a bijective proof is obtained; however, no explicit status evidence field is supplied for this candidate.
References
Primary source
Kaimei Huang and Sherry H. F. Yan, “Further results on r-Euler-Mahonian statistics”, arXiv:2501.12083 (2025).
Additional references
2 papers in this index state this conjecture (2024–2025). The statement above is taken from the most recent of them; the others are arXiv:2408.04185.
Progress summary
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Solutions 0
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