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Details for article 6 of 9 found articles
| Title: |
Permanents of convex combinations of doubly stochastic matrices |
| Author: |
Foregger, Thomas H. |
| Appeared in: |
Linear & multilinear algebra |
| Paging: | Volume 23 (1988) nr. 1 pages 79-90 |
| Year: |
1988-03 |
| Contents: |
Let S be a 4 × 4 doubly stochastic matrix and t0 < t ≥ 4/3, where t0 is the unique real root of 106t3 - 418t2 + 465t - 100. We prove that per(tJ4 + (1 - t)S) ≤ per(S) with equality if and only if S = J4. This confirms for n = 4 a conjecture of K. Lih and E. T. H. Wang that for [image omitted] . We also show that another conjecture of K. Lih and E. T. H. Wang, per(tjn + (1 - t) S) ≤ t per(Jn) + (1 - t) per(S) for t ε [1/2, 1] is true for n = 4 and t ε [t2, 1], where t2 is the unique real root of 106t3 - 418t2 + 465t - 153. Note that t2 is about 0.6216986477375. Finally, we exhibit a set of 4 × 4 doubly stochastic matrices for which per(tJ4 + (1 - t)A) is a strictly decreasing function of t on (0,4/3] whenever A is a member of the set. This answers a question raised by H. Minc. |
| Publisher: |
Taylor & Francis |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 6 of 9 found articles
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