A generalization of Eulerian numbers via rook placements
Copyright policy )A generalization of Eulerian numbers via rook placements
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 $k$.
15 pages
- University of Notre Dame United States
- Iowa State University United States
- Emory University United States
- College of Saint Benedict and Saint John's University United States
- Carnegie Mellon University United States
juggling, Exact enumeration problems, generating functions, multiplex, 05A15, 05A10, recursion, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05A15, Eulerian numbers
juggling, Exact enumeration problems, generating functions, multiplex, 05A15, 05A10, recursion, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05A15, Eulerian numbers
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