General global maximum conjecture for the rank-two likelihood model

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Let n≥2n\ge2 and let s,ts,t satisfy 0<t<s0<t<s. For positive uu and positive integer block dimensions, write (u)l1×l2(u)_{l_1\times l_2} for the l1×l2l_1\times l_2 matrix all of whose entries equal uu. Let L(P)L(P) be the likelihood function defined in the source by equation (newLP). General likelihood conjecture. The matrix

P=1ns+(n−1)nt((s−t⌈n/2⌉+t)⌈n/2⌉×⌈n/2⌉(t)⌈n/2⌉×⌊n/2⌋(t)⌊n/2⌋×⌈n/2⌉(s−t⌊n/2⌋+t)⌊n/2⌋×⌊n/2⌋)P=\frac{1}{ns+(n-1)nt}\begin{pmatrix}\left(\frac{s-t}{\lceil n/2\rceil}+t\right)_{\lceil n/2\rceil\times\lceil n/2\rceil}&(t)_{\lceil n/2\rceil\times\lfloor n/2\rfloor}\\(t)_{\lfloor n/2\rfloor\times\lceil n/2\rceil}&\left(\frac{s-t}{\lfloor n/2\rfloor}+t\right)_{\lfloor n/2\rfloor\times\lfloor n/2\rfloor}\end{pmatrix}

is a global maximum for L(P)L(P).

This is the paper's proposed extension from the four-by-four case to arbitrary nn. The source does not reproduce the definition of L(P)L(P) in the supplied context, and its discussion says that an efficient method for n>4n>4 is lacking.

References

Primary source

Mingfu Zhu, Guangran Jiang and Shuhong Gao, “Solving the 100 Swiss Francs Problem”, arXiv:0809.4627 (2011).

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