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Volumn 18, Issue 1, 2004, Pages 103-109

Small examples of nonconstructible simplicial balls and spheres

Author keywords

Constructibility; Knots in 3 balls and 3 spheres; Shellability; Simplicial balls and spheres; Vertex decomposability

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL GEOMETRY; MATHEMATICAL MODELS; THEOREM PROVING; TOPOLOGY;

EID: 14644417147     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480103430521     Document Type: Article
Times cited : (21)

References (36)
  • 1
    • 0000429934 scopus 로고
    • The combinatorial theory of complexes
    • J. W. ALEXANDER, The combinatorial theory of complexes, Ann. of Math. (2), 31 (1930), pp. 292-320.
    • (1930) Ann. of Math. (2) , vol.31 , pp. 292-320
    • Alexander, J.W.1
  • 4
    • 0003193239 scopus 로고
    • Some aspects of the topology of 3-manifolds related to the Poincaré conjecture
    • T. L. Saaty, ed., John Wiley & Sons, New York
    • R. H. BING, Some aspects of the topology of 3-manifolds related to the Poincaré conjecture, in Lectures on Modern Mathematics, Vol. II, T. L. Saaty, ed., John Wiley & Sons, New York, 1964, pp. 93-128.
    • (1964) Lectures on Modern Mathematics , vol.2 , pp. 93-128
    • Bing, R.H.1
  • 5
    • 0000956933 scopus 로고
    • Topological methods
    • R. Graham, M. Grötschel, and L. Lovász, eds., Elsevier, Amsterdam
    • A. BJÖRNER, Topological methods, in Handbook of Combinatorics, R. Graham, M. Grötschel, and L. Lovász, eds., Elsevier, Amsterdam, 1995, pp. 1819-1872.
    • (1995) Handbook of Combinatorics , pp. 1819-1872
    • Björner, A.1
  • 6
    • 0034360439 scopus 로고    scopus 로고
    • Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincaré homology 3-sphere
    • A. BJÖRNER AND F. H. LUTZ, Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincaré homology 3-sphere, Experiment. Math., 9 (2000), pp. 275-289.
    • (2000) Experiment. Math. , vol.9 , pp. 275-289
    • Björner, A.1    Lutz, F.H.2
  • 9
    • 0000916326 scopus 로고
    • Shellable decompositions of cells and spheres
    • H. BRUGGESSER AND P. MANI, Shellable decompositions of cells and spheres, Math. Scand., 29 (1971), pp. 197-205.
    • (1971) Math. Scand. , vol.29 , pp. 197-205
    • Bruggesser, H.1    Mani, P.2
  • 10
    • 0002439897 scopus 로고
    • Shrinking cell-like decompositions of manifolds. Codimension three
    • J. W. CANNON, Shrinking cell-like decompositions of manifolds. Codimension three, Ann. of Math. (2), 110 (1979), pp. 83-112.
    • (1979) Ann. of Math. (2) , vol.110 , pp. 83-112
    • Cannon, J.W.1
  • 11
    • 84972217679 scopus 로고
    • A convex 3-complex not simplicially isomorphic to a strictly convex complex
    • R. CONNELLY AND D. W. HENDERSON, A convex 3-complex not simplicially isomorphic to a strictly convex complex, Math. Proc. Cambridge Philos. Soc., 88 (1980), pp. 299-306.
    • (1980) Math. Proc. Cambridge Philos. Soc. , vol.88 , pp. 299-306
    • Connelly, R.1    Henderson, D.W.2
  • 12
    • 0039126304 scopus 로고
    • Which spheres are shellable?
    • Algorithmic Aspects of Combinatorics, B. Alspach, P. Hell, and D. J. Miller, eds., North-Holland, Amsterdam
    • G. DANARAJ AND V. KLEE, Which spheres are shellable?, in Algorithmic Aspects of Combinatorics, Ann. Discrete Math. 2, B. Alspach, P. Hell, and D. J. Miller, eds., North-Holland, Amsterdam, 1978, pp. 33-52.
    • (1978) Ann. Discrete Math. , vol.2 , pp. 33-52
    • Danaraj, G.1    Klee, V.2
  • 15
    • 0040722648 scopus 로고
    • Zur Grundlegung der kombinatorischen Topologie
    • R. FURCH, Zur Grundlegung der kombinatorischen Topologie, Abh. Math. Sem. Univ. Hamburg, 3 (1924), pp. 69-88.
    • (1924) Abh. Math. Sem. Univ. Hamburg , vol.3 , pp. 69-88
    • Furch, R.1
  • 17
    • 0033470118 scopus 로고    scopus 로고
    • Nonconstructible simplicial balls and a way of testing constructibility
    • M. HACHIMORI, Nonconstructible simplicial balls and a way of testing constructibility, Discrete Comput. Geom., 22 (1999), pp. 223-230.
    • (1999) Discrete Comput. Geom. , vol.22 , pp. 223-230
    • Hachimori, M.1
  • 18
    • 0034397018 scopus 로고    scopus 로고
    • Decompositions of simplicial balls and spheres with knots consisting of few edges
    • M. HACHIMORI AND G. M. ZIEGLER, Decompositions of simplicial balls and spheres with knots consisting of few edges, Math. Z., 235 (2000), pp. 159-171.
    • (2000) Math. Z. , vol.235 , pp. 159-171
    • Hachimori, M.1    Ziegler, G.M.2
  • 19
    • 0001662527 scopus 로고
    • Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes
    • M. HÖCHSTER, Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes, Ann. of Math. (2), 96 (1972), pp. 318-337.
    • (1972) Ann. of Math. (2) , vol.96 , pp. 318-337
    • Höchster, M.1
  • 21
    • 0023455578 scopus 로고
    • The d-step conjecture and its relatives
    • V. KLEE AND P. KLEINSCHMIDT, The d-step conjecture and its relatives, Math. Oper. Res., 12 (1987), pp. 718-755.
    • (1987) Math. Oper. Res. , vol.12 , pp. 718-755
    • Klee, V.1    Kleinschmidt, P.2
  • 22
    • 14644420516 scopus 로고
    • An unsplittable triangulation
    • W. B. R. LICKORISH, An unsplittable triangulation, Michigan Math. J., 18 (1971), pp. 203-204.
    • (1971) Michigan Math. J. , vol.18 , pp. 203-204
    • Lickorish, W.B.R.1
  • 23
    • 0009048856 scopus 로고
    • Unshellable triangulations of spheres
    • W. B. R. LICKORISH, Unshellable triangulations of spheres, European J. Combin., 12 (1991), pp. 527-530.
    • (1991) European J. Combin. , vol.12 , pp. 527-530
    • Lickorish, W.B.R.1
  • 28
    • 84976163829 scopus 로고
    • The maximum numbers of faces of a convex polytope
    • P. MCMULLEN, The maximum numbers of faces of a convex polytope, Mathematika, 17 (1970), pp. 179-184.
    • (1970) Mathematika , vol.17 , pp. 179-184
    • McMullen, P.1
  • 29
    • 9944237411 scopus 로고
    • On the foundations of combinatory analysis situs I, II
    • M. H. A. NEWMAN, On the foundations of combinatory analysis situs I, II, Proc. Royal Acad. Amsterdam, 29 (1926), pp. 611-626, 627-641.
    • (1926) Proc. Royal Acad. Amsterdam , vol.29 , pp. 611-626
    • Newman, M.H.A.1
  • 30
    • 0040722651 scopus 로고
    • A property of 2-dimensional elements
    • M. H. A. NEWMAN, A property of 2-dimensional elements, Proc. Royal Acad. Amsterdam, 29 (1926), pp. 1401-1405.
    • (1926) Proc. Royal Acad. Amsterdam , vol.29 , pp. 1401-1405
    • Newman, M.H.A.1
  • 31
    • 0040310476 scopus 로고
    • Decompositions of simplicial complexes related to diameters of convex polyhedra
    • J. S. PROVAN AND L. J. BILLERA, Decompositions of simplicial complexes related to diameters of convex polyhedra, Math. Oper. Res., 5 (1980), pp. 576-594.
    • (1980) Math. Oper. Res. , vol.5 , pp. 576-594
    • Provan, J.S.1    Billera, L.J.2
  • 32
    • 0039855549 scopus 로고
    • An unshellable triangulation of a tetrahedron
    • M. E. RUDIN, An unshellable triangulation of a tetrahedron, Bull. Amer. Math. Soc., 64 (1958), pp. 90-91.
    • (1958) Bull. Amer. Math. Soc. , vol.64 , pp. 90-91
    • Rudin, M.E.1
  • 33
    • 4244118371 scopus 로고
    • Theorie der vielfachen Kontinuität
    • Zürcher und Furrer, Zürich, 1901 (written 1850-1852). Reprinted in Ludwig Sohläfli 1814-1895, Gesammelte mathematische Abhandlungen, Band I, Birkhäuser, Basel
    • L. SCHLÄFLI, Theorie der vielfachen Kontinuität, Neue Denkschriften der allgemeinen schweizerischen Gesellschaft für die Gesammten Naturwissenschaften 38, Zürcher und Furrer, Zürich, 1901 (written 1850-1852). Reprinted in Ludwig Sohläfli 1814-1895, Gesammelte mathematische Abhandlungen, Band I, Birkhäuser, Basel, 1950, pp. 167-387.
    • (1950) Neue Denkschriften der Allgemeinen Schweizerischen Gesellschaft für die Gesammten Naturwissenschaften , vol.38 , pp. 167-387
    • Schläfli, L.1
  • 34
    • 0040773847 scopus 로고
    • A non-shellable 3-sphere
    • A. VINCE, A non-shellable 3-sphere, European J. Combin., 6 (1985), pp. 91-100.
    • (1985) European J. Combin. , vol.6 , pp. 91-100
    • Vince, A.1
  • 35
    • 0003222229 scopus 로고
    • Lectures on polytopes
    • Springer-Verlag, New York; revised edition, 1998
    • G. M. ZIEGLER, Lectures on Polytopes, Grad. Texts in Math. 152, Springer-Verlag, New York, 1995; revised edition, 1998.
    • (1995) Grad. Texts in Math. , vol.152
    • Ziegler, G.M.1
  • 36
    • 0032374426 scopus 로고    scopus 로고
    • Shelling polyhedral 3-balls and 4-polytopes
    • G. M. ZIEGLER, Shelling polyhedral 3-balls and 4-polytopes, Discrete Comput. Geom., 19 (1998), pp. 159-174.
    • (1998) Discrete Comput. Geom. , vol.19 , pp. 159-174
    • Ziegler, G.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.