Chris Ormerod 2007 J. Phys. A: Math. Theor. 40 12799 doi:10.1088/1751-8113/40/42/S22
Chris Ormerod
Show affiliationsWe present theory outlining associated linear problems for ultradiscrete equations. The appropriate domain for these problems is the max-plus semiring. Our main result is that despite the restrictive nature of the max-plus semiring, it is still possible to define a theory of connection matrices analogous to that of Birkhoff and his school for systems of linear difference equations. We use such theory to provide evidence for the integrability of an ultradiscrete difference equation.
39A13 Difference equations, scaling (q-differences) (See also 33Dxx)
15A24 Matrix equations and identities
34M55 Painlevé and other special equations; classification, hierarchies; isomonodromic deformations
Issue 42 (19 October 2007)
Received 6 December 2006, in final form 7 March 2007
Published 2 October 2007
Chris Ormerod 2007 J. Phys. A: Math. Theor. 40 12799
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