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The minimal Hilbert basis of the Hammond order cone

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  • Ramses H. Abul Naga

    (Universidad de Málaga
    University of Aberdeen
    Pan African Scientific Research Council)

Abstract

We characterize the minimal Hilbert basis of the Hammond order cone, and present several novel applications of the resulting basis. From the basis, we extract an invertible matrix, that provides a numerical representation of the Hammond order relation. The basis also enables the construction of a space—that we call the Hammond order lattice—where order-extensions of the Hammond order (i.e. more complete relations) may be derived. Finally, we introduce a class of maximal linearly independent Hilbert bases, in which the specific results derived in relation to the Hammond order cone, are shown to hold more generally.

Suggested Citation

  • Ramses H. Abul Naga, 2022. "The minimal Hilbert basis of the Hammond order cone," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 191-215, October.
    • Handle: RePEc:spr:etbull:v:10:y:2022:i:2:d:10.1007_s40505-022-00226-2
    DOI: 10.1007/s40505-022-00226-2
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