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Dual rook polynomials

✍ Scribed by Markus Fulmek

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 732 KB
Volume: 177
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00357-3

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✦ Synopsis

A theorem contained in the paper 'A combinatoric formula' by Wang, Lee and Tan (J. Math. Anal. Appl. 160 (1991) 500--503) gives rise to the definition of certain polynomials associated with boards: Stimulated by the analogy to the well-known rook polynomials, we call them 'dual rook polynomials'. We show that in the cases of Ferrers boards and skew boards the evaluation of these polynomials at -1 always yields values -1,0 or 1, generalizing the theorem cited above. Moreover, we evaluate these polynomials at -2. Finally, we state three conjectures that are quite well supported by empirical tests: Two of these conjectures are known to be true for rook polynomials.

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