한국수학사학회지 (Journal for History of Mathematics)

한국수학사학회 (The Korean Society for History of Mathematics)
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열대평면곡선의 여러 가지 성질에 대한 연구

A Study on Various Properties of Tropical Plane Curves

  • Kim, Young Rock (Math. Edu., Graduate School of Edu., Hankuk Univ. of Foreign Studies) ;
  • Shin, Yong-Su (Dept. of Math., Sungshin Women's Univ.)
  • 투고 : 2016.09.01
  • 심사 : 2016.10.30
  • 발행 : 2016.10.31
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초록

In tropical geometry, the sum of two numbers is defined as the minimum, and the multiplication as the sum. We learned that dynamic programming in tropical algebraic geometry can be used to find the shortest path in graphs. We have also learned about the Bezout's Theorem, which is a theorem concerning the intersections of tropical plane curves, and the stable intersection principle.

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참고문헌

  1. Francois Louis BACCELLI, Guy COHEN, Geert Jan OLSDER, and Jean- Pierre QUADRAT, Synchronization and linearity, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons Ltd., Chichester, 1992. An algebra for discrete event systems.
  2. I. M. GELFAND, M. M. KAPRANOV, and A. V. ZELEVINSKY, Discriminants, resultants and multidimensional determinants, Modern Birkhauser Classics. Birkhauser Boston Inc., Boston, MA, 2008. Reprint of the 1994 edition.
  3. Ilia ITENBERG, Gregory MIKHALKIN, and Eugenii SHUSTIN, Tropical Algebraic geometry, Birkhauser, 2009.
  4. Diane MACLAGAN and Bernd STURMFELS Introduction to Tropical Geometry, Graduate Studies in Mathematics 161, Americal Mathematical Society, 2015.
  5. Jean-Eric PIN, Tropical semirings, In Idempotency (Bristol, 1994), volume 11 of Publ. Newton Inst., 50-69. Cambridge Univ. Press, Cambridge, 1998.
  6. Imre SIMON, Recognizable sets with multiplicities in the tropical semiring, In Mathematical foundations of computer science, 1988 (Carlsbad, 1988), volume 324 of Lecture Notes in Comput. Sci., 107-120, Springer, Berlin, 1988.
  7. David SPEYER and Bernd STURMFELS, Tropical Mathematics, Mathematics Magazine 82(3) (2009), 163-173. https://doi.org/10.4169/193009809X468760

피인용 문헌

  1. 열대곡선 헤아리기 vol.30, pp.3, 2016, https://doi.org/10.14477/jhm.2017.30.3.185