Inequalities in Products of Minors of Totally Nonnegative Matrices

  • Authors:

  • Mark Skandera

  • Affiliations:

  • Department of Mathematics, Dartmouth College, 6188 Bradley Hall, Hanover, NH 03755-3551, USA. mark.skandera@dartmouth.edu

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2004

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Abstract

Let ΔI,I′ be the minor of a matrix which corresponds to row set I and column set I′. We give a characterization of the inequalities of the formΔI,I′ ΔK,K′ ≤ ΔJ,J′ ΔL,L′which hold for all totally nonnegative matrices. This generalizes a recent result of Fallat, Gekhtman, and Johnson.