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Nonattacking Queens in a Rectangular Strip | | Seth Chaiken
; Christopher R.H. Hanusa
; Thomas Zaslavsky
; | | Date: |
25 May 2011 | | Abstract: | The function that counts the number of ways to place nonattacking identical
chess or fairy chess pieces in a rectangular strip of fixed height and variable
width, as a function of the width, is a piecewise polynomial which is
eventually a polynomial and whose behavior can be described in some detail. We
deduce this by converting the problem to one of counting lattice points outside
an affinographic hyperplane arrangement, which Forge and Zaslavsky solved by
means of weighted integral gain graphs.
We extend their work by developing both generating functions and a detailed
analysis of deletion and contraction for weighted integral gain graphs.
For chess pieces we find the asymptotic probability that a random
configuration is nonattacking, and we obtain exact counts of nonattacking
configurations of small numbers of queens, bishops, knights, and nightriders. | | Source: | arXiv, 1105.5087 | | Services: | Forum | Review | PDF | Favorites | |
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