The hyperdeterminant and triangulations of the 4-cube

Mathematics of Computation

Volumn 77, Issue 263, 2008, Pages 1653-1679

  Huggins, Peter ^a   Sturmfels, Bernd ^b   Yu, Josephine ^c   Yuster, Debbie S ^d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c Och Spine at New York Presbyterian Hospitals   (United States)

^d RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 47249159040     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-08-02073-5     Document Type: Article

References (22)

1. E. Allman and J. Rhodes: Phylogenetic invariants for stationary base composition, Journal Symbolic Computation 41 (2006) 138-150. MR2197150 (2006j:92041)
2. F. Block and J. Yu: Tropical convexity via cellular resolutions, Journal of Algebraic Combinatorics 24 (2006) 103-114. MR2245783 (2007f:52041)
3. R. W. Cottle: Minimal triangulation of the 4-cube, Discrete Math. 40 (1982) 25-29. MR676709 (84d:05065a)
4. A. Conca, S. Hosten and R. Thomas: Nice initial complexes of some classical ideals, Algebraic and geometric combinatorics, Contemp. Math., 423, Amer. Math. Soc., Providence, RI, 2006, pp. 11-42. MR2298753
5. D. Cox, J. Little and D. O'Shea: Using Algebraic Geometry, Graduate Texts in Mathematics 185, second edition, Springer Verlag, New York, 2005. MR2122859 (2005i:13037)
6. J. De Loera: Nonregular triangulations of products of simplices, Discrete and Computational Geometry 15 (1996) 253-264. MR1380393 (97i:52017)
7. V. de Silva and L.-H. Lim: Tensor rank and the ill-posedness of the best low-rank approximation problem, SIAM Journal on Matrix Analysis and Applications, to appear.
8. A. Dickenstein, E.M. Feichtner and B. Sturmfels: Tropical discriminants, Journal of the American Mathematical Society, 20 (2007) 1111-1133.
9. M. Develin and B. Sturmfels: Tropical convexity, Documenta Math. 9 (2004) 1-27. MR2054977 (2005i:52010)
10. J. De Loera, J. Rambau and F. Santos: Triangulations: Applications, Structures and Algorithms, Algorithms and Computation in Mathematics, Springer Verlag, Heidelberg, to appear.
11. E. Gawrilow and M. Joswig: Polymake: a framework for analyzing convex polytopes, in Polytopes - Combinatorics and Computation, eds. G. Kalai and G.M. Ziegler, Birkhäuser, 2000, pp. 43-74. MR1785292 (2001f:52033)
12. I.M. Gel'fand, M.M. Kapranov, A.V. Zelevinsky: Discriminants, Resultants, and Multidimensional Determinants; Birkhäuser, Boston, MA, 1994. MR1264417 (95e:14045)
13. H. Hirai: A geometric study of the split decomposition, Discrete and Computational Geometry 36(2006) 331-361. MR2252108 (2007f:52025)
14. P. Lévay: On the geometry of a class of N-qubit entanglement monotones, Journal of Physics A 38(2005) 9075-9085. MR2185885 (2006m:81070)
15. J.-G. Luque and J.-Y. Thibon: The polynomial invariants of four qubits, Phys. Rev. A 67, 042303(2003). MR2039690 (2004k:81098)
16. J. Pfeifle and J. Rambau: Computing triangulations using oriented matroids, in Algebra, Geometry and Software Systems (M. Joswig and N. Takayama, eds.) Springer Verlag, 2003, pp. 49-76. MR2011753 (2004i:68233)
17. J. Rambau: TOPCOM: triangulations of point configurations and oriented matroids. Mathematical Software (Beijing, 2002), World Sci. Publishing, River Edge, NJ, 2002, 330-340. MR1932619
18. F. Santos: The Cayley trick and triangulations of products of simplices, In Integer Points in Polyhedra - Geometry, Number Theory, Algebra, Optimization, (eds. A. Barvinok, M. Beck, C. Haase, B. Reznick, and V. Welker), Contemporary Mathematics 374, Amer. Math. Soc., Providence, 2005. MR2134757 (2005j:00018)
19. B. Sturmfels and S. Sullivant: Combinatorial secant varieties, Quarterly Journal of Pure and Applied Mathematics, 2 (2006) 285-309, (Special issue: In Honor of Robert MacPherson). MR2252121
20. B. Sturmfels and J. Yu: Classification of six-point metrics, Electronic Journal of Combinatorics 11 (2004/05) R44. MR2097310 (2005m:51016)
21. J.G. Sumner and P.D. Jarvis: Using the tangle: a consistent construction of phylogenetic distance matrices for quartets, Math. Biosci. 204 (2006) 49-67. MR2269665 (2007g:92057)
22. J.M.F. ten Berge: Kruskal's polynomial for 2 x 2 x 2-arrays and a generalization to 2 x n x n-arrays, Psychometrika 58 (1991) 631-636.