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math.CO2021
Proof of a Conjecture on Hankel Determinants for Dyck Paths with Restricted Peak Heights
Guoce Xin, Zihao Zhang
For any integer and , let denote the number of -Dyck paths whose peak's heights are for some integer . We find the generati…
math.CO2021
Enumerating Magic Distinct Labellings of the Cube
Guoce Xin, Yingrui Zhang, Zihao Zhang
We find by applying MacMahon's partition analysis that all magic labellings of the cube are of eight types, each generated by six basis elements. A combinatorial proof of this fact…