Rook Number
The rook numbers 
of an 
Board 
are the number of subsets of size 
such that no twoelements have the same first or second coordinate. In other word, it is the number of ways of placing rooks on such that none attack each other. The rook numbers of a board determine the rook numbers of the complementary board
, defined to be 
. This is known as the Rook Reciprocity Theorem. The first few rook numbers are 1, 2, 7, 23, 115, 694, 5282, 46066, ... (Sloane's A000903). For an board, each Permutation Matrix corresponds to an allowed configuration of rooks.
References
Sloane, N. J. A. SequenceA000903/M1761in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
- Pearls of Sluze
- Pear-Shaped Curve
- Pearson-Cunningham Function
- Pearson Kurtosis
- Pearson Mode Skewness
- Pearson's Correlation
- Pearson's Function
- Pearson Skewness
- Pearson's Skewness Coefficients
- Pearson System
- Pearson Type III Distribution
- Peaucellier Cell
- Peaucellier Inversor
- Peaucellier's Linkage
- Pedal
- Pedal Circle
- Pedal Coordinates
- Pedal Curve
- Pedal Line
- Pedal Point
- Pedal Triangle
- Peg Knot
- Peg Solitaire
- Peg Top
- Peirce's Theorem