Cycle products and efficient vectors in reciprocal matrices
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913422362279936 |
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| author | Furtado, Susana Johnson, Charles |
| author_facet | Furtado, Susana Johnson, Charles |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10481 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cycle products and efficient vectors in reciprocal matrices Furtado, Susana Johnson, Charles Combinatorics 15B48, 05C20, 90B50, 91B06 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. |
| title | Cycle products and efficient vectors in reciprocal matrices |
| topic | Combinatorics 15B48, 05C20, 90B50, 91B06 |
| url | https://arxiv.org/abs/2312.10481 |