REFERENCES
- Butkovic , P. ( 2003 ). Max-algebra: the linear algebra of combinatorics? Lin. Alg. and Appl. 313 – 335 .
- Cuninghame-Green , R. , Butkovic , P. ( 2004 ). Bases in max-algebra . Linear Algebra and its Applications 389 : 107 – 120 .
- Develin , M. , Santos , F. , Sturmfels , B. ( 2004 ). On the rank of a tropical matrix . Preprint at arXiv:math.CO/0312114 .
- Gathmann , A. ( 2006 ). Tropical algebraic geometry . Preprint at arXiv:math.AG/0601322, January .
- Golan , J. ( 1992 ). The Theory of Semirings with Applications in Mathematics and Theoretical Computer Science . Vol. 54 . Longman Sci & Tech.
- Itenberg , I. , Mikhalkin , G. , Shustin , E. ( 2007 ). Tropical Algebraic Geometry . Vol. 35 . Oberwolfach seminars : Birkhauser .
- Kim , K. H. , Roush , F. W. ( 2005 ). Kapranov rank vs. tropical rank . Preprint at arXiv:math.CO/0503044, March .
- Lallement , G. ( 1979 ). Semigroups and Combinatorial Applications . New York : John Wiley & Sons, Inc.
- Lawler , E. L. ( 1976 ). Combinatorial Optimization: Networks and Matroids . Holt, Rinehart, and Winston .
- Margolis , S. W. , Pin , J.-E . ( 1987 ). Inverse semigroups and extensions of groups by semilattices . J. Algebra 110 : 277 – 297 .
- Mikhalkin , G. ( 2006 ). Atropical geometry and its applications . In: Sanz-Solé , et al. ., eds. Proceedings of the ICM, Madrid, Spain , Vol. II . August 22–30, 2006. Invited lectures . Zürich : European Math. Soc. , pp. 827 – 852 .
- Richter-Gebert , J. , Sturmfels , B. , Theobald , T. (2005). First steps in tropical geometry. Idempotent Mathematics and Mathematical Physics . pp. 289–317, Providence, RI : Contemp. Math. Amer. Math. Soc. p. 377.
- Shustin , E. ( 2005 ). A tropical approach to enumerative geometry . Algebra i Analiz 17 ( 2 ): 170 – 214 .
- Speyer , D. , Sturmfels , B. ( 2004a ). Tropical grassmannians . Adv. Geom. 4 ( 3 ): 389 – 411 .
- Speyer , D. E. , Sturmfels , B. ( 2004b ). Tropical mathematics . Preprint at arXiv:math. CO/0408099 .
- Communicated by M. Cohen.