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arXiv · 2312.10481

Cycle products and efficient vectors in reciprocal matrices

Susana Furtado·Charles Johnson
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Abstract

We focus upon the relationship between Hamiltonian cycle products and efficient vectors for a reciprocal matrix $A$, to more deeply understand the latter. This facilitates a new description of the set of efficient vectors (as a union of convex subsets), greater understanding of convexity within this set and of order reversals in efficient vectors. A straightforward description of all efficient vectors for an $n$-by-$n$, column perturbed consistent matrix is given; it is the union of at most $(n-1)$ choose $2$ convex sets.

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Susana Furtado, Charles Johnson. 2024-07-09. Cycle products and efficient vectors in reciprocal matrices. https://arxiv.org/abs/2312.10481

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