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Proofs of two conjectures of Berkovich and Dhar on hook lengths
Rong Chen
We prove stronger forms of two conjectures of Berkovich and Dhar concerning a coefficientwise inequality and pairs of hooks of length two in bounded partitions. The coefficientwise…
Two-colored generalized Frobenius partitions and minimal-excludant sums over bipartitions
Rong Chen, Kang-Yu Wang, Yi-ning Wang
Let $\cpsi_{2,a}(n)$ denote the number of -colored Frobenius partitions of weight , where the two rows have prescribed length difference. We study the two cases and…
Combinatorial proofs for partitions with repeated smallest part
Dandan Chen, Rong Chen, Mengjie Zhao
Recently, Andrews and El Bachraoui considered the number of integer partitions whose smallest part is repeated exactly times and the remaining parts are not repeated. They pres…
A conjecture of Radu and Sellers on congruences modulo powers of 2 for broken 3-diamond partitions
Dandan Chen, Rong Chen, Siyu Yin
In 2007, Andrews and Paule introduced the family of functions , which enumerate the number of broken -diamond partitions for a fixed positive integer . In 2013, Radu…
On the total number of ones associated with cranks of partitions modulo 11
Dandan Chen, Rong Chen, Siyu Yin
In 2021, Andrews mentioned that George Beck introduced partition statistics , which denote the total number of ones in the partition of with crank congruent to …