R. Merris, The permanental dominance conjecture, Current Trends in Matrix Theory (R. Grone and F. Uhlig, eds.), Elsevier, New York, 1987, pp 213-223. Research supported by ONR contract 85K0335.

Conjecture 6 was affirmed by R. Grone and S. Pierce, SIAM J. Matrix Anal. Appl. 9 (1988), 194-201.

This article was written in conjunction with the author's talk at the Third Auburn Matrix Theory Conference, 19-22 March 1986. It seems to have been instrumental in reviving interest in the permanental dominance conjecture. Among the publications citing it are

  • G. D. James and M. W. Liebeck, Proc. London Math. Soc. 55 (1987), 243-265.
  • H. Minc, Linear & Multilinear Algebra 21 (1987), 109-148.
  • R. B. Bapat, Linear & Multilinear Algebra 23 (1988), 55-62.
  • M. Marcus and M. Sandy, Linear & Multilinear Algebra 23 (1988), 233-249.
  • T. Pate, Linear & Multilinear Algebra 24 (1989), 135-149.
  • P. Heyfron, Linear & Multilinear Algebra 32 (1992), 75-84.
  • C. F. Chan, Linear & Multilinear Algebra 27 (1990), 189-198.
  • P. Heyfron, Math. Proc. Cambridge Philos. Soc. 109 (1991), 15-30.
  • J. Bunce, Linear & Multilinear Algebra 30 (1991), 5-11.
  • M. Marcus, Linear Algebra Appl. 150 (1991), 41-59.
  • T. Pate, Linear & Multilinear Algebra 31 (1992), 27-36.
  • R. B. Bapat, Linear & Multilinear Algebra 32 (1992), 335-337.
  • T. Pate, Linear Algebra Appl. 161-164 (1992), 639-650.
  • C. Greene, Linear Algebra Appl. 171 (1992), 65-79.
  • A. Krauter, Jahrbuch Uberbliche Mathematik (1992), 185-201.
  • A. K. Lal, Coxeter Groups and Positive Matrices, Ph.D. Thesis, Indian Statistical Institute, New Delhi, 1992.
  • W. Watkins, Linear Algebra Appl. 181 (1993), 1-28.
  • G. Soules, Linear Algebra Appl. 201 (1994), 211-229.
  • R. B. Bapat and A. K. Lal, Linear Algebra Appl. 198 (1994), 397-409.
  • T. Pate, Linear & Multilinear Algebra 38 (1995), 295-307.
  • T. Pate, Linear Algebra Appl. 254 (1997), 427-466.
  • T. Pate, Linear Algebra Appl. 255 (1997), 203-242.
  • R. B. Bapat and T. E. S. Raghavan, Nonnegative Matrices and Applications, Encyclopedia of Mathematics and Its Applications 64, Cambridge University Press, 1997.
  • A. K. Lal, Linear Algebra Appl. 274 (1998), 1-16.
  • T. Pate, Proc. London Math. Soc. 76 (1998), 307-358.
  • F. Zhang, Matrix Theory Basic Results and Techniques, Springer, New York, 1999.
  • T. Pate, Linear Algebra Appl. 295 (1999), 31-59.
  • P. Diaconis and S. N. Evans, J. Combinatorial Theory (A) 91 (2000), 305-321.
  • T. H. Pate, Linear & Multilinear Algebra 51 (2003), 263-278.
  • Gi-Sang Cheon and Ian M. Wanless, Linear Algebra Appl. (2005), 314-342.