Abstract
We present an explicit solution of the Ar 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.
Original language | English (US) |
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Pages (from-to) | 1-43 |
Number of pages | 43 |
Journal | Electronic Journal of Combinatorics |
Volume | 17 |
Issue number | 1 |
State | Published - 2010 |
Externally published | Yes |
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics