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Falsity of Wang's conjecture on stars

✍ Scribed by C.S.Karuppan Chetty; S.Maria Arulraj

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
276 KB
Volume
277
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

Let Q,, denote the set of all n x n doubly stochastic matrices. E.T.H. Wang called a matrix B C Q,, a star if per(:cB + ( 1 -:Β’)A) ~< cΒ’ per(B) + (1 ~) per(A) for all A C f~. and for all :~ E [0, 1] and conjectured in 1979 that for n/> 3, permutation matrices are the only stars. In this paper we disprove Wang's conjecture for n = 3, by showing that PBQ is a star where E X ';1 ~1, 0~<x~<l B= 1-x and P and Q are permutation matrices. We also establish that the only stars in Q3 are PBQ as defined above.

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