Geodesic
Solutions to the T-systems with principal coefficients
Panupong Vichitkunakorn1
1University of Illinois at Urbana-Champaign
The electronic journal of combinatorics, Tome 23 (2016) no. 2
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The $A_\infty$ T-system, also called the octahedron recurrence, is a dynamical recurrence relation. It can be realized as mutation in a coefficient-free cluster algebra (Kedem 2008, Di Francesco and Kedem 2009). We define T-systems with principal coefficients from cluster algebra aspect, and give combinatorial solutions with respect to any valid initial condition in terms of partition functions of perfect matchings, non-intersecting paths and networks. This also provides a solution to other systems with various choices of coefficients on T-systems including Speyer's octahedron recurrence (Speyer 2007), generalized lambda-determinants (Di Francesco 2013) and (higher) pentagram maps (Schwartz 1992, Ovsienko et al. 2010, Glick 2011, Gekhtman et al. 2016).
DOI : 10.37236/5698
Classification : 05E10, 05C70, 82B20
Mots-clés : discrete dynamical systems, dimers, paths, networks

Panupong Vichitkunakorn  1

1 University of Illinois at Urbana-Champaign 
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Panupong Vichitkunakorn. Solutions to the T-systems with principal coefficients. The electronic journal of combinatorics, Tome 23 (2016) no. 2. doi: 10.37236/5698

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