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Rook polynomials
in three and higher dimensions
Feryal Alayont and Nicholas Krzywonos
Vol. 6 (2013), No. 1, 35–52
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Abstract |
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The rook polynomial of a board counts the number of ways of placing nonattacking rooks on the board. In this paper, we describe how the properties of the two-dimensional rook polynomials generalize to the rook polynomials of “boards” in three and higher dimensions. We also define families of three-dimensional boards which generalize the two-dimensional triangle boards and the boards representing the problème des rencontres. The rook coefficients of these three-dimensional boards are shown to be related to famous number sequences such as the central factorial numbers, the number of Latin rectangles and the Genocchi numbers. |
Keywords
rook polynomial, three dimensions, central factorial
numbers, Genocchi numbers, problème des rencontres
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Mathematical Subject Classification 2010
Primary: 05A05, 05A10
Secondary: 11B73
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Milestones
Received: 15 September 2011
Accepted: 30 May 2012
Published: 23 June 2013
Communicated by Jim Haglund
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Authors |
| Feryal Alayont | |
| Department of Mathematics Grand Valley State University 1 Campus Drive Allendale, MI 49401 United States |
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| Nicholas Krzywonos | |
| Department of Mathematics Grand Valley State University 1 Campus Drive Allendale, MI 49401 United States |
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