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Q-matrix recognition via secondary and universal polytopes

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(Mx+q)=0, Mx+q≥0, x≥0 has a solution. We explain how one can use the polyhedral structure of the set of all triangulations of a finite point set to determine if an n×n matrix M is a Q-matrix. Our implementation of the algorithm is practical for deciding the Q-nature for all M with n≤8.

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Authors and Affiliations

  1. The Geometry Center and School of Mathematics, University of Minnesota, Minneapolis MN 55454, e-mail: deloera@geom.umn.edu, , , , , , US

    Jesús A. De Loera

  2. Department of Mathematical Sciences, George Mason University, Fairfax, Virginia, 22030, e-mail: wmorris@osf1.gmu.edu, , , , , , US

    Walter D. Morris jr.

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  1. Jesús A. De Loera
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  2. Walter D. Morris jr.
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Received May 30, 1997 / Revised version received June 12, 1998 Published online November 24, 1998

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De Loera, J., Morris jr., W. Q-matrix recognition via secondary and universal polytopes. Math. Program. 85, 259–276 (1999). https://doi.org/10.1007/s101070050057

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  • DOI: https://doi.org/10.1007/s101070050057

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