The solution of the $A_r$ T-system for arbitrary boundary

Details The solution of the $A_r$ T-system for arbitrary boundary The solution of the $A_r$ T-system for arbitrary boundary

2010-02-23

arxiv.org/abs/1002.4427v1

Elec. Jour. of Comb. Vol. 17(1) (2010) R89

Mathematics

Combinatorics

42 pages, 33 figures

Scientific paper

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.

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