Geodesic
The solution of the A\(_{r}\) T-system for arbitrary boundary
The electronic journal of combinatorics, Tome 17 (2010)
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We present an explicit solution of the $A_r$ $T$-system for arbitrary boundary conditions. For each boundary, this is done by constructing a network, i.e. a graph with positively weighted edges, and the solution is expressed as the partition function for a family of non-intersecting paths on the network. This proves in particular the positive Laurent property, namely that the solutions are all Laurent polynomials of the initial data with non-negative integer coefficients.
DOI : 10.37236/361
Classification : 05C25, 13F60 
@article{10_37236_361,
     author = {Philippe Di Francesco},
     title = {The solution of the {A\(_{r}\)} {T-system} for arbitrary boundary},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/361},
     zbl = {1230.05153},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/361/}
}
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Philippe Di Francesco. The solution of the A\(_{r}\) T-system for arbitrary boundary. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/361

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