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Volumn 100, Issue 1, 2002, Pages 1-26

A polytopal generalization of sperner's lemma

Author keywords

Path following; Polytopes; Simplicial algorithms; Sperner's lemma

Indexed keywords


EID: 0036798681     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcta.2002.3274     Document Type: Article
Times cited : (41)

References (24)
  • 1
    • 0011019654 scopus 로고    scopus 로고
    • Combinatorial bases in systems of simplices and chambers
    • T. V. Alekseyevskaya, Combinatorial bases in systems of simplices and chambers, Discrete Math. 157 (1996), 15-37.
    • (1996) Discrete Math , vol.157 , pp. 15-37
    • Alekseyevskaya, T.V.1
  • 3
    • 84972570711 scopus 로고
    • A proof of the lower bound conjecture for convex polytopes
    • D. Barnette, A proof of the lower bound conjecture for convex polytopes, Pacific J. Math. 46 (1973), 349-354.
    • (1973) Pacific J. Math , vol.46 , pp. 349-354
    • Barnette, D.1
  • 6
    • 0034415121 scopus 로고    scopus 로고
    • Minimal simplicial dissections and triangulations of convex 3-polytopes
    • A. Below, U. Brehm, J. A. De Loera, and J. Richter-Gebert, Minimal simplicial dissections and triangulations of convex 3-polytopes, Discrete Comput. Geom. 24 (2000), 35-48.
    • (2000) Discrete Comput. Geom , vol.24 , pp. 35-48
    • Below, A.1    Brehm, U.2    De Loera, J.A.3    Richter-Gebert, J.4
  • 7
    • 0000657027 scopus 로고    scopus 로고
    • Extremal properties for dissections of convex 3-polytopes
    • J. A. De Loera, F. Santos, and F. Takeuchi, Extremal properties for dissections of convex 3-polytopes, SIAM J. Discrete Math. 14 (2001), 143-161.
    • (2001) SIAM J. Discrete Math , vol.14 , pp. 143-161
    • De Loera, J.A.1    Santos, F.2    Takeuchi, F.3
  • 8
    • 0001419975 scopus 로고
    • On the Sperner lemma
    • D. I. A. Cohen, On the Sperner lemma, J. Combin. Theory 2 (1967), 585-587.
    • (1967) J. Combin. Theory , vol.2 , pp. 585-587
    • Cohen, D.I.A.1
  • 9
    • 85031386364 scopus 로고    scopus 로고
    • Reference deleted in proof
    • Reference deleted in proof.
  • 10
    • 38249006486 scopus 로고
    • Combinatorial analogs of Brouwer's fixed-point theorem on a Bounded polyhedron
    • R. M. Freund, Combinatorial analogs of Brouwer's fixed-point theorem on a Bounded polyhedron, J. Combin. Theory Ser. B 47 (1989), 192-219.
    • (1989) J. Combin. Theory Ser. B , vol.47 , pp. 192-219
    • Freund, R.M.1
  • 11
    • 85031386108 scopus 로고    scopus 로고
    • Reference deleted in proof
    • Reference deleted in proof.
  • 12
    • 0000574179 scopus 로고
    • Ein Beweis des Fixpunktsatzes für n-dimensionale Simplexe
    • B. Knaster, C. Kuratowski, and S. Mazurkiewicz, Ein Beweis des Fixpunktsatzes für n-dimensionale Simplexe, Fund. Math. 14 (1929), 132-137.
    • (1929) Fund. Math , vol.14 , pp. 132-137
    • Knaster, B.1    Kuratowski, C.2    Mazurkiewicz, S.3
  • 13
    • 0001011343 scopus 로고
    • Simplicial approximation of fixed points
    • H. W. Kuhn, Simplicial approximation of fixed points, Proc. Natl. Acad. Sci. 61 (1968), 1238-1242.
    • (1968) Proc. Natl. Acad. Sci , vol.61 , pp. 1238-1242
    • Kuhn, H.W.1
  • 15
    • 85031374862 scopus 로고    scopus 로고
    • "Combinatorial Proofs of Generalizations of Sperner's Lemma"
    • Senior thesis, Harvey Mudd College
    • E. Peterson, "Combinatorial Proofs of Generalizations of Sperner's Lemma," Senior thesis, Harvey Mudd College, 2000.
    • (2000)
    • Peterson, E.1
  • 16
    • 51249173383 scopus 로고
    • On triangulations of the convex hull of n points
    • B. L. Rothschild and E. G. Straus, On triangulations of the convex hull of n points, Combinatorica 5 (1985), 167-179.
    • (1985) Combinatorica , vol.5 , pp. 167-179
    • Rothschild, B.L.1    Straus, E.G.2
  • 17
    • 0001310049 scopus 로고
    • The approximation of fixed points of a continuous mapping
    • H. Scarf, The approximation of fixed points of a continuous mapping, SIAM J. Appl. Math. 15 (1967), 1328-1343.
    • (1967) SIAM J. Appl. Math , vol.15 , pp. 1328-1343
    • Scarf, H.1
  • 18
    • 85031382146 scopus 로고    scopus 로고
    • Consensus-halving via theorems of Borsuk-Ulam and Tucker
    • preprint
    • F. W. Simmons and F. E. Su, Consensus-halving via theorems of Borsuk-Ulam and Tucker, preprint.
    • Simmons, F.W.1    Su, F.E.2
  • 19
    • 0034406112 scopus 로고    scopus 로고
    • A lower bound for the simplexity of the n-cube via hyperbolic volumes, special issue: Combinatorics of polytopes
    • W. D. Smith, A lower bound for the simplexity of the n-cube via hyperbolic volumes, special issue: Combinatorics of polytopes, European J. Combin. 21 (2000), 131-137.
    • (2000) European J. Combin , vol.21 , pp. 131-137
    • Smith, W.D.1
  • 20
    • 0000549502 scopus 로고
    • Neuer Beweis für die Invarianz der Dimensionszahl und des Gebietes
    • E. Sperner, Neuer Beweis für die Invarianz der Dimensionszahl und des Gebietes, Abh. Math. Sem. Univ. Hamburg 6 (1928), 265-272.
    • (1928) Abh. Math. Sem. Univ. Hamburg , vol.6 , pp. 265-272
    • Sperner, E.1
  • 21
    • 0033482214 scopus 로고    scopus 로고
    • Rental harmony: Sperner's lemma in fair division
    • F. E. Su, Rental harmony: Sperner's lemma in fair division, Amer. Math. Monthly 106 (1999), 930-942.
    • (1999) Amer. Math. Monthly , vol.106 , pp. 930-942
    • Su, F.E.1
  • 23
    • 0003564656 scopus 로고    scopus 로고
    • "Computing Equilibria and Fixed Points" 23
    • Kluwer Academic Publishers, Boston
    • Z. Yang, "Computing Equilibria and Fixed Points," Kluwer Academic Publishers, Boston, 1999.
    • (1999)
    • Yang, Z.1
  • 24
    • 0003589701 scopus 로고
    • "Lectures on Polytopes"
    • Springer-Verlag, New York
    • G. M. Ziegler, "Lectures on Polytopes," Springer-Verlag, New York, 1995.
    • (1995)
    • Ziegler, G.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.