The rook problem on saw-toothed chessboards
نویسندگان
چکیده
منابع مشابه
The rook problem on saw-toothed chessboards
A saw-toothed chessboard, or STC for short, is a kind of chessboard whose boundary forms two staircases from left down to right without any hole inside it. A rook at square (i, j) can dominate the squares in row i and in column j . The rook problem of an STC is to determine the minimum number of rooks that can dominate all squares of the STC. In this paper, we model an STC by two particular gra...
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Abstract. For an element w in the Weyl algebra generated by D and U with relation DU = UD + 1, the normally ordered form is w = ∑ ci,jU D . We demonstrate that the normal order coefficients ci,j of a word w are rook numbers on a Ferrers board. We use this interpretation to give a new proof of the rook factorization theorem, which we use to provide an explicit formula for the coefficients ci,j ....
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2008
ISSN: 0893-9659
DOI: 10.1016/j.aml.2007.12.003