Advanced search
Publication Cover
Linear and Multilinear Algebra Volume 67, 2019 - Issue 6
Submit an article Journal homepage
128
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

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

Hui-li WangSchool of Sciences, Southwest Petroleum University, Chengdu, China.;Institute of Nonlinear Dynamics, Southwest Petroleum University, Chengdu, China.Correspondence[email protected]
View further author information
&
Yan YangSchool of Sciences, Southwest Petroleum University, Chengdu, China.View further author information
Pages 1103-1108 | Received 12 Nov 2017, Accepted 21 Feb 2018, Published online: 27 Feb 2018

References

  • Shinzawa N . Ultra discrete permanent and the consistency of max plus linear equations. Linear Algebra Appl. 2016;506:445–477.
  • Plus M . Linear systems in (max, +)-algebra. In: Proceedings of the 29th Conference on Decision and Control, Honolulu; 1990 Dec.
  • Kuniba A , Sakamoto R , Yamada Y . Tau functions in combinatorial Bethe ansatz. Nuclear Phys. B. 2007;786:207–266.
  • Takahashi D , Hirota R . Ultradiscrete soliton solution of permanent type. J Phys Soc Jpn. 2007;76:104007.
  • Takahashi D , Satsuma J . A soliton cellular automaton. J Phys Soc Jpn. 1990;59:3514.
  • Tokihiro T , Takahashi D , Matsukidaira J . From soliton equations to integrable cellular automata through a limiting procedure. Phys Rev Lett. 1996;76:3247.
  • Tokihiro T , Takahashi D , Matsukidaira J . Box and ball system as a realization of ultradiscrete nonautonomous KP equation. J Phys A. 2000;33:607–619.
  • Richter-Gebert J , Sturmfels B , Theobald T . First steps in tropical geometry. In: Litvinov GL , Maslov VP , editors. Idempotent mathematics and mathematical physics. Vol. 377, Contemporary mathematics. Providence (RI): American Mathematical Society; 2005. p. 289–317.
  • Cuninghame-Green RA . Projections in minimax algebra. Math Program. 1976;10(1):111–123.
  • Engel GM , Schneider H . Cyclic and diagonal products on a matrix. Linear Algebra Appl. 1973;7:301–335.
  • Cuninghame-Green RA . Minimax algebra. Vol. 166, Lecture notes in economics and mathematical systems. Berlin: Springer-Verlag; 1979.
  • Butkovič P . Max-linear systems: theory and algorithms. London: Springer-Verlag; 2010.
  • Wang X , Wang H . The generators of the solution space for a system of inequalities. Linear Algebra Appl. 2014;459:248–263.
  • Wang H , Wang X . A polynomial algorithm for solving system of inequalities in max-plus algebra. Inform Sci. 2015;318:1–13.
  • Sergeev S . Extremals of the supereigenvector cone in max algebra: a combinatorial description. Linear Algebra Appl. 2015;479:106–117.
  • Butkovič P . On tropical supereigenvectors. Linear Algebra Appl. 2016;498:574–591.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.