A note on the paper ‘Ultra discrete permanent and the consistency of max plus linear equations’

Abstract

This work is concerned with the consistency conditions for the equations in max plus algebra. The three classes of the max plus linear equations presented in the paper Shinzawa [Ultra discrete permanent and the consistency of max plus linear equations, Linear Algebra Appl. 506 (2016) 445–477] can be equivalently converted into the corresponding system of inequalities. The equivalence relation between ultra discrete permanent and maximum cycle mean is suggested. Thus, the necessary and sufficient conditions for solvability of the equations are obtained using the maximum cycle mean in this note.

Keywords:

• Max plus algebra
• equations
• inequalities
• finite solution

AMS Subject Classifications:

• 15A80
• 15A06
• 15A39

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11401494] and Youth Science and Technology Innovation Team of Southwest Petroleum University for Nonlinear Systems [grant number 2017CXTD02] and Science and Technology Innovation Team of Education Department of Sichuan for Dynamical System and its Applications [grant number 18TD0013].