2007/12/11 by Kasraoui, Anisse, Zeng, Jiang
#05A15 #05A30 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.0712.1755
We study statistics on ordered set partitions whose generating functions are related to p,q-Stirling numbers of the second kind. The main purpose of this paper is to provide bijective proofs of all the conjectures of \stein (Arxiv:math.CO/0605670). Our basic idea is to encode ordered partitions by a kind of path diagrams and explore the rich combinatorial properties of the latter structure. We also give a partition version of MacMahon's theorem on the equidistribution of the statistics inversion number and major index on words.