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math.CO2024
Generalizations of wreath product identities via Garsia-Gessel bijections
Tingyao Xiong
Garsia and Gessel constructed innovative bijections to obtain multivariate generating functions of permutation statistics. In 2011, Biaogioli and Zeng successfully derived four and…
math.CO2014★ 1 cited
Combinatorial Interpretation of General Eulerian Numbers
Tingyao Xiong, Jonathan I. Hall, Hung-ping Tsao
Since 1950s, mathematicians have successfully interpreted the traditional Eulerian numbers and Eulerian numbers combinatorially. In this paper, the authors give a combinatorial…
math.CO2012★ 1 cited
General Eulerian Numbers and Eulerian Polynomials
Tingyao Xiong, Hung-ping Tsao, Jonathan I. Hall
In this paper, we will define general Eulerian numbers and Eulerian polynomials based on general arithmetic progressions. Under the new definitions, we have been successful in exte…