Queens Independence Separation on Rectangular Chessboards

Sowndarya Suseela Padma Kaluri, Y Lakshmi Naidu

Abstract


The famous eight queens problem with non-attacking queens placement on an 8 x 8 chessboard was first posed in the year 1848. The queens separation problem is the legal placement of the fewest number of pawns with the maximum number of independent queens placed on an N x N board which results in a separated board. Here a legal placement is defined as the separation of attacking queens by pawns. Using this concept, the current study extends the queens separation problem onto the rectangular board M x N, (M<N),  to result in a separated board with the maximum number of independent queens. The research work here first describes the  M+k queens separation with k=1 pawn and continue to find for any k. Then it  focuses on finding the symmetric solutions of the M+k queens separation with k pawns.

Full Text:

PDF

References


Cairns, G., Queens on Non-square Tori, The Electronic Journal of Combinatorics, 8(2001), 1-3.

Chatham, R. D., Reflections on the N + k Queens problem, College Math. J., 40 (2009), 204-210.

Chatham, R. D., Doyle, M., Fricke, G. H., Reitmann, J., Skaggs, R. D., and Wolff, M., Independence and domination separation on chessboard graphs, J. Combin. Math. Combin.

Comput., 68 (2009), 3-17.

Chatham, R. D., Fricke, G. H., and Skaggs, R. D., The queens separation problem, Util. Math., 69 (2006), 129-141.

Chatham, R. D., Doyle, M., Jeffers, R. J., Kosters, W. A., Skaggs, R. D., and Ward, J., Centrosymmetric solutions to chessboard separation problems, Bulletin of the Institute of

Combinatorics and its Applications, 65 (2012), 6-26.

Zhao, K., The Combinatorics of Chessboards, Ph.D. dissertation, City University of New York, (1998).




DOI: https://doi.org/10.22342/jims.27.2.986.158-169

Refbacks

  • There are currently no refbacks.



Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
Senolowo, Sinduadi, Mlati, Sleman Regency, Special Region of Yogyakarta 55281, Telp. (0274) 552243
Email: jims.indoms@gmail.com


p-ISSN: 2086-8952 | e-ISSN: 2460-0245


Journal of the Indonesian Mathematical Society is licensed under a Creative Commons Attribution 4.0 International License

web statistics
View My Stats