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A catalog of minimally nonideal matrices

Author

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  • Christine Lütolf
  • François Margot

Abstract

This paper describes a backtracking algorithm for the enumeration of nonisomorphic minimally nonideal (n ×n) matrices that are not degenerate projective planes. The application of this algorithm forn ≤ 12 yielded 20 such matrices, adding 5 matrices to the 15 previously known. For greater dimensions,n=14 andn=17, 13 new matrices are given. For nonsquare matrices, 38 new minimally nonindeal matrices are described. Copyright Physica-Verlag 1998

Suggested Citation

  • Christine Lütolf & François Margot, 1998. "A catalog of minimally nonideal matrices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(2), pages 221-241, June.
    • Handle: RePEc:spr:mathme:v:47:y:1998:i:2:p:221-241
    DOI: 10.1007/BF01194398
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    Cited by:

    1. Gabriela Argiroffo & Silvia Bianchi & Graciela Nasini, 2008. "Some insight into characterizations of minimally nonideal matrices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 245-256, April.
    2. Conforti, Michele & Cornuejols, Gerard & Kapoor, Ajai & Vuskovic, Kristina, 2001. "Perfect, ideal and balanced matrices," European Journal of Operational Research, Elsevier, vol. 133(3), pages 455-461, September.
    3. Ahmad Abdi & Ricardo Fukasawa & Laura Sanità, 2018. "Mathematics of Operations Research," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 428-459, May.

    More about this item

    Keywords

    nonideal matrices; backtracking;

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