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Rook Reciprocity Theorem

sum_(k=0)^dr_k^B(d-k)!x^k=sum_(k=0)^d(-1)^kr_k^(B^_)(d-k)!x^k(x+1)^(d-k).

See also

Rook Polynomial

References

Chow, T. Y. "The Path-Cycle Symmetric Function of a Digraph." Adv. Math. 118, 71-98, 1996.Chow, T. "A Short Proof of the Rook Reciprocity Theorem." Electronic J. Combinatorics 3, No. 1, R10, 1-2, 1996. http://www.combinatorics.org/Volume_3/Abstracts/v3i1r10.html.Goldman, J. R.; Joichi, J. T.; and White, D. E. "Rook Theory I. Rook Equivalence of Ferrers Boards." Proc. Amer. Math. Soc. 52, 485-492, 1975.Riordan, J. An Introduction to Combinatorial Analysis. New York: Wiley, 1958.

Referenced on Wolfram|Alpha

Rook Reciprocity Theorem

Cite this as:

Weisstein, Eric W. "Rook Reciprocity Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RookReciprocityTheorem.html