The four-dimensional Perfect-Mirsky Conjecture
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- by Jeremy Levick, Rajesh Pereira and David W. Kribs
- Proc. Amer. Math. Soc. 143 (2015), 1951-1956
- DOI: https://doi.org/10.1090/S0002-9939-2014-12412-9
- Published electronically: December 15, 2014
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Abstract:
We verify the Perfect-Mirsky Conjecture on the structure of the set of eigenvalues for all $n \times n$ doubly stochastic matrices in the four-dimensional case. The $n=1,2,3$ cases have been established previously and the $n=5$ case has been shown to be false. Our proof is direct and uses basic tools from matrix theory and functional analysis. Based on this analysis we formulate new conjectures for the general case.References
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Bibliographic Information
- Jeremy Levick
- Affiliation: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1
- Rajesh Pereira
- Affiliation: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1
- David W. Kribs
- Affiliation: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1
- Received by editor(s): May 29, 2013
- Received by editor(s) in revised form: June 28, 2013, and November 11, 2013
- Published electronically: December 15, 2014
- Communicated by: Pamela B. Gorkin
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 1951-1956
- MSC (2010): Primary 15B51; Secondary 15A18, 46A55, 46H05
- DOI: https://doi.org/10.1090/S0002-9939-2014-12412-9
- MathSciNet review: 3314105