A generalization of Eulerian numbers via rook placements

@article{Banaian2015AGO,
title={A generalization of Eulerian numbers via rook placements},
author={Esther Banaian and Steve Butler and Christopher Cox and Jeffrey Davis and Jacob Landgraf and Scarlitte Ponce},
journal={arXiv: Combinatorics},
year={2015}
}
• Published 14 August 2015
• Mathematics
• arXiv: Combinatorics
We consider a generalization of Eulerian numbers which count the number of placements of $cn$ "rooks" on an $n\times n$ board where there are exactly $c$ rooks in each row and each column, and exactly $k$ rooks below the main diagonal. The standard Eulerian numbers correspond to the case $c=1$. We show that for any $c$ the resulting numbers are symmetric and give generating functions of these numbers for small values of $k$.
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References

SHOWING 1-6 OF 6 REFERENCES
A symmetrical Eulerian identity
• Mathematics
• 2010
We find a q-analog of the following symmetrical iden- tity involving binomial coefficients n m � and Eulerian numbers n m � : X
Concrete mathematics - a foundation for computer science
• Education
• 1989
From the Publisher: This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid
Juggling Drops and Descents
• Mathematics
• 1994
(1994). Juggling Drops and Descents. The American Mathematical Monthly: Vol. 101, No. 6, pp. 507-519.
, and Donald Knuth , A symmetrical Eulerian identity
• Journal of Combinatorics
Him Haglund , and Jeffrey Remmel , Rook Theory Notes , manuscript