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Minimum permanents on two faces of the polytope of doubly stochastic matrices

โœ Scribed by Kyle Pula; Seok-Zun Song; Ian M. Wanless

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
151 KB
Volume
434
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

We consider the minimum permanents and minimising matrices on the faces of the polytope of doubly stochastic matrices whose nonzero entries coincide with those of, respectively,

.

Here J r,s denotes the r ร— s matrix all of whose entries are 1, I n is the identity matrix of order n and 0 m is the m ร— m zero matrix. We conjecture that V m,n is cohesive but not barycentric for 1 < n < m + โˆš m and that it is not cohesive for n m + โˆš m. We prove that it is cohesive for 1 < n < m + โˆš m and not cohesive for n 2m and confirm the conjecture computationally for n < 2m 200. We also show that U m,n is barycentric.

๐Ÿ“œ SIMILAR VOLUMES

Minimum permanents on a face of the poly
Minimum permanents on a face of the polytope of doubly stochastic matrices
โœ Seok-Zun Song; Sung Min Hong; Young-Bae Jun; Seon-Jeong Kim ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 619 KB

For n 3 6, we determine the minimum permanents and minimizing matrices on the faces of R3+,, the polytope of (3 + n) x (3 + n) doubly stochastic matrices. whose nonzero entries coincide with those of where J is the matrix with all entries equal 1, I the identity matrix, and 0 the zero matrix.