P.L.-spheres, convex polytopes, and stress

Discrete and Computational Geometry

Volumn 15, Issue 4, 1996, Pages 389-421

  Lee, C W ^a  

^a UNIVERSITY OF KENTUCKY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040304596     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02711516     Document Type: Article

References (24)

1. D. W. Barnette, The minimum number of vertices of a simple polytope, Israel J. Math., 10 (1971), 121-125.
2. D. W. Barnette, A proof of the lower bound conjecture for convex polytopes, Pacific J. Math., 46 (1973), 349-354.
3. L. J. Billera and C. W. Lee, The numbers of faces of polytope pairs and unbounded polyhedra, European J. Combin., 2 (1981), 307-322.
4. P. Filliman, Face numbers of pl-spheres, Manuscript, 1991.
5. P. Filliman, Rigidity and the Alexandro v-Fenchel inequality, Monatsh. Math., 113 (1992), 1-22.
6. W. Fulton, Introduction to Toric Varieties, Annals of Mathematics Studies, Vol. 131, Princeton University Press, Princeton, NJ, 1993.
7. d. Part I: Necessity of Eckhoff's conditions, Israel J. Math., 48 (1984), 175-195.
8. G. Kalai, Rigidity and the lower bound theorem. I, Invent. Math., 88 (1987), 125-151.
9. B. Kind and P. Kleinschmidt, Schälbare Cohen-Macauley-Komplexe und ihre Parametrisierung, Math. Z., 167 (1979), 173-179.
10. C. W. Lee, Some recent results on convex polytopes, Contemp. Math., 114 (1990), 3-19.
11. C. W. Lee, Generalized stress and motions,in Polytopes:Abstract, Convex and Computational, T. Bistriczky, P. McMullen, R. Schneider, and A. I. Weiss, eds., NATO ASI Series C, Vol. 440, Kluwer, Dordrecht, 1994, pp. 249-271.
12. P. McMullen, The maximum numbers of faces of a convex polytope, Mathematika, 17 (1970), 179-184.
13. P. McMullen, On simple polytopes, Invent. Math., 113 (1993), 419-444.
14. P. McMullen, Weights on polytopes, Discrete Comput. Geom., this issue, pp. 363-388.
15. P. McMullen and D. W. Walkup, A generalized lower-bound conjecture for simplicial polytopes, Mathematika, 18 (1971), 264-273.
16. T. Oda, Convex Bodies and Algebraic Geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), Vol. 15 [Results m Mathematics and Related Areas (3)], Springer-Verlag, Berlin, 1988.
17. T. Oda, Convex Bodies and Algebraic Geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), Vol. 15 [Results m Mathematics and Related Areas (3)], Springer-Verlag, Berlin, 1988.
18. U. Pachner, Shellings of simplicial balls and p.l. manifolds with boundary, Discrete Math., 81 (1990), 37-47.
19. G. Reisner, Cohen-Macaulay quotients of polynomial rings, Adv. in Math., 21 (1976), 30-49.
20. R. P. Stanley, The upper bound conjecture and Cohen-Macaulay rings, Stud. Appl. Math., 54 (1975), 135-142.
21. R. P. Stanley, Hilbert functions of graded algebras, Adv. in Math., 28 (1978), 57-83.
22. R. P. Stanley, The number of faces of a simplicial convex polytope, Adv. in Math., 35 (1980), 236-238.
23. T.-S. Tay, N. White, and W. Whiteley, Skeletal rigidity of simplicial complexes, I, II, European J. Combin., 16 (1995), 381-403, 503-523.
24. T.-S. Tay, N. White, and W. Whiteley, A homological interpretation of skeletal rigidity, Manuscript, 1993.