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- William Y. C. Chen, James J. Y. Zhao
- Discrete Mathematics
- 2005

We show that the formalism of overpartitions gives a simple involution for the product definition of the Gaussian coefficients. In the formulation of our involution, an overline in the representation of an overpartition is endowed with a weight.

- James J. Y. Zhao
- Electr. J. Comb.
- 2013

The Alladi-Gordon identity ∑j k=0(q i−k+1; q)k [ j k ] q(i−k)(j−k) = 1 plays an important role for the Alladi-Gordon generalization of Schur’s partition theorem. By using Joichi-Stanton’s insertion algorithm, we present an overpartition interpretation for the Alladi-Gordon key identity. Based on this interpretation, we further obtain a combinatorial proof… (More)

- James J. Y. Zhao
- Electr. J. Comb.
- 2015

Based on the combinatorial proof of Schur’s partition theorem given by Bressoud, and the combinatorial proof of Alladi’s partition theorem given by Padmavathamma, Raghavendra and Chandrashekara, we obtain a bijective proof of a partition theorem of Alladi, Andrews and Gordon.

- Linyuan Lu, Arthur L. B. Yang, James J. Y. Zhao
- WAW
- 2016

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