Q-Counting rook configurations and a formula of Frobenius
Journal of Combinatorial Theory Series A
p,q-Stirling numbers and set partition statistics
Journal of Combinatorial Theory Series A
Interpolating set partition statistics
Journal of Combinatorial Theory Series A
&sgr;-restricted growth functions and p, q-Stirling numbers
Journal of Combinatorial Theory Series A
The combinatorics of q-Charlier polynomials
Journal of Combinatorial Theory Series A
Juggling and applications to q-analogues
Proceedings of the 6th conference on Formal power series and algebraic combinatorics
Regular Article: New Euler驴Mahonian Statistics on Permutations and Words
Advances in Applied Mathematics
Euler-Mahonian Statistics on Ordered Set Partitions
SIAM Journal on Discrete Mathematics
New Wilf-equivalence results for vincular patterns
European Journal of Combinatorics
Separation of variables and combinatorics of linearization coefficients of orthogonal polynomials
Journal of Combinatorial Theory Series A
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[E. Steingrimsson, Statistics on ordered partitions of sets, arXiv: math.CO/0605670] introduced several hard statistics on ordered set partitions and conjectured that their generating functions are related to the q-Stirling numbers of the second kind. In a previous paper, half of these conjectures have been proved by Ishikawa, Kasraoui and Zeng using the transfer-matrix method. In this paper, we shall give bijective proofs of all the conjectures of Steingrimsson. Our basic idea is to encode ordered set partitions by a kind of path diagrams and explore the rich combinatorial properties of the latter structure. As a bonus of our approach, we derive two new @s-partition interpretations of the p,q-Stirling numbers of the second kind introduced by Wachs and White. We also discuss the connections with MacMahon's theorem on the equidistribution of the inversion number and major index on words and give a partition version of his result.