In 2011, Biaogioli and Zeng successfully derived four and six variate distributions via Garsia-Gessel’s bijections, by defining a “Biaogioli-Zeng’s ordering” on the set of wreath product Zr ≀ Sn. In this paper, we will prove that B-Z’s four-variate identities can be generalized to any positive-dominant ordering.
Keywords: Wreath product, Biagioli-Zeng’s ordering, positive-dominant ordering, multivariate joint distributions.

Dr. Tingyao Xiong, is currently an Associate Professor at Radford University, U.S.A. She got her Bachelor’s Degree in Mathematics from Nanjing University in China. She continued her study in Mathematics and Statistics at Michigan State University, where she got her Ph.D. degree under the supervision of Professor Jonathan Hall. Dr. Xiong’s Ph.D. dissertation was funded by U.S. NSF with award # 0601621. Dr. Xiong is an active scholar with wide research interest in area of Number Theory, Combinatorics, Information Theory and Financial Mathematics. She has given presentations on various international conferences including AMS Joint Meeting and IEEE ISIT.