#### Vol. 10, No. 4, 2017

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A generalization of Eulerian numbers via rook placements

### Esther Banaian, Steve Butler, Christopher Cox, Jeffrey Davis, Jacob Landgraf and Scarlitte Ponce

Vol. 10 (2017), No. 4, 691–705
##### Abstract

We consider a generalization of Eulerian numbers which count the number of placements of $cn$ rooks on an $n×n$ chessboard 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 $k$.

##### Keywords
Eulerian numbers, juggling, recursion, multiplex
Primary: 05A15