R. Grone, R. Merris, and W. Watkins, Cones in the group algebra related to Schur's determinantal inequality, Rocky Mtn. J. Math. 18 (1988), 137-146. AMS Abstracts 7 (1986), 30. Math Reviews 89e:15011. Research supported by ONR contract 85K0335.

Let c be a complex valued function of the symmetric group S_n and denote by d_c the corresponding complex valued function of the n-by-n matrices. This article concerns the cone C = {c: d_c(A) >= 0 for all psdh matrices A}. The extreme rays of this cone have implications for the permanental dominance conjecture. Among the publications citing this article are

  • W. Watkins, Linear Algebra Appl. 181 (1993), 1-28.
  • T. H. Pate, Linear Algebra Appl. 212/213 (1994), 31-44.
  • T. H. Pate, Linear Algebra Appl. 291 (1999), 201-225.
  • T. H. Pate, Linear & Multilinear Algebra 51 (2003), 361-391.