Inequalities in Products of Minors of Totally Nonnegative Matrices
Mark Skandera
DOI: 10.1023/B:JACO.0000047282.21753.ae
Abstract
Let 
I, 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 form I, I K, K 
J, J L, L
I, 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 form I, I K, K J, J L, L Pages: 195–211
Keywords: nonnegative matrices; inequalities of products
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References
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2. C.W. Cryer, “Some properties of totally positive matrices,” Lin. Alg. Appl. 15 (1976), 1-25.
3. S.M. Fallat, M.I. Gekhtman, and C.R. Johnson, “Multiplicative principal-minor inequalities for totally nonnegative matrices,” Adv. Appl. Math. (2002).
4. S. Fomin and A. Zelevinsky, “Total positivity: Tests and parametrizations,” Math. Intelligencer (2001), 23-33.
5. I. Gessel and G. Viennot, “Binomial determinants, paths, and hook length formulae,” Advances in Mathematics 58 (1985), 300-321.
6. I. Gessel and G. Viennot, “Determinants and plane partitions,”
1989. Preprint.
7. S. Karlin and G. McGregor, “Coincidence probabilities,” Pacific J. Math. 9 (1959), 1141-1164.
8. B. Lindstr\ddot om, “On the vector representations of induced matroids,” Bull. London Math. Soc. 5 (1973), 85-90.
9. C. Loewner, “On totally positive matrices,” Math. Z. 63 (1955), 338-340.
10. G. Lusztig, “Total positivity in reductive groups,” in Lie Theory and Geometry: In Honor of Bertram Kostant, vol. 123 of Progress in Mathematics. Birkh\ddot auser, Boston, 1994, pp. 531-568.
11. R. Stanley, Enumerative Combinatorics, vol.
2. Cambridge University Press, Cambridge, 1999.
12. A. Whitney, “A reduction theorem for totally positive matrices,” J. d'Analyse Math. 2 (1952), 88-92.
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