The solution of the Ar T-system for arbitrary boundary

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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 languageEnglish (US)
Pages (from-to)1-43
Number of pages43
JournalElectronic Journal of Combinatorics
Volume17
Issue number1
StatePublished - Aug 20 2010
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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