R. Merris and W. Watkins, Inequalities and identities for generalized matrix functions, Linear Algebra Appl. 64 (1985), 223-242. Research supported by NSF grant MCS 83-00097. AMS Abstracts 4 (1983), 582. Math Reviews 86e:15007.

This article shows how to express the immanant of a matrix as a sum of products of permanents of complementary principal submatrices, with an application to the permanental dominance conjecture.

Evidence supporting the conjecture on page 230 can be found in [T. H. Pate, Psi-functions, irreducible characters and a conjecture of Merris and Watkins, Linear and Multilinear Algebra 35 (1993), 195-212].

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  • R. Grone, Linear Algebra Appl. 68 (1985), 252-254.
  • R. Grone, Linear & Multilinear Algebra 18 (1985), 147-152.
  • W. Watkins, Linear & Multilinear Algebra 20 (1986), 75-86.
  • H. Minc, Linear & Multilinear Algebra 21 (1987), 109-148.
  • C. R. Johnson and S. Pierce, Linear & Multilinear Algebra 21 (1987), 215-229.
  • G. D. James and M. Liebeck, Proc. London Math. Soc. 55 (1987), 243-265.
  • P. Heyfron, Linear & Multilinear Algebra 24 (1988), 65-78.
  • C. R. Johnson and S. Pierce, Linear Algebra Appl. 102 (1988), 55-79.
  • T. Pate, Linear & Multilinear Algebra 28 (1990), 175-184.
  • T. Pate, Trans. Amer. Math. Soc. 325 (1991), 875-894.
  • T. Pate, Linear Algebra Appl. 162-164 (1992), 639-650.
  • R. D. Poshusta and D. B. Kinghorn, Internat'l J. Quantum Chemistry 41 (1992), 15-42.
  • W. W. Barrett and C. R. Johnson, Linear & Multilinear Algebra 34 (1993), 67-74.
  • T. Pate, J. London Math. Soc. 49 (1994), 40-60.
  • T. Pate, Linear Algebra Appl. 212/213 (1994), 31-44.
  • 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.
  • O. Chan and T. K. Lam, Linear Algebra Appl. 261 (1997), 23-47.
  • G. James, C.R.Johnson, and S. Pierce, J. London Math. Soc. 57 (1998), 562-582.
  • T. Pate, Proc. London Math. Soc. 76 (1998), 307-358.
  • T. Pate, Linear Algebra Appl. 295 (1999), 31-59.
  • G. G. Cash, J. Chem. Inf. & Comp. Sci. 43 (2003), 1942-1946.
  • J. A. Dias da Silva and M. M. Torres, Linear Algebra Appl. 401 (2005), 77-107.