Combinatorial lemmas for polyhedrons

• Autorzy: Adam Idzik , Konstanty Junosza-Szaniawski
• Języki publikacji: EN

Abstrakty

EN

We formulate general boundary conditions for a labelling to assure the existence of a balanced n-simplex in a triangulated polyhedron. Furthermore we prove a Knaster-Kuratowski-Mazurkiewicz type theorem for polyhedrons and generalize some theorems of Ichiishi and Idzik. We also formulate a necessary condition for a continuous function defined on a polyhedron to be an onto function.

Słowa kluczowe

EN

KKM covering; labelling; primoid; pseudomanifold; simplicial complex; Sperner lemma

Kategorie tematyczne

• 47H10: Fixed-point theorems
• 05B30: Other designs, configurations
• 54H25: Fixed-point and coincidence theorems
• 52A20: Convex sets in n dimensions (including convex hypersurfaces)

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2005
• Tom: 25
• Numer: 1-2
• Strony: 95-102

Daty

wydano

2005

Twórcy

autor

Adam Idzik

• Akademia Świetokrzyska, 15 Świetokrzyska street, 25-406 Kielce, Poland
• Institute of Computer Science, Polish Academy of Sciences, 21 Ordona street, 01-237 Warsaw, Poland

autor

Konstanty Junosza-Szaniawski

• Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland

Bibliografia

• [1] T. Ichiishi and A. Idzik, Closed coverings of convex polyhedra, Internat. J. Game Theory 20 (1991) 161-169, doi: 10.1007/BF01240276.
• [2] T. Ichiishi and A. Idzik, Equitable allocation of divisible goods, J. Math. Econom. 32 (1998) 389-400, doi: 10.1016/S0304-4068(98)00053-6.
• [3] A. Idzik and K. Junosza-Szaniawski, Combinatorial lemmas for nonoriented pseudomanifolds, Top. Meth. in Nonlin. Anal. 22 (2003) 387-398.
• [4] B. Knaster, C. Kuratowski and S. Mazurkiewicz, Ein beweis des fixpunktsatzes für n-dimensionale simplexe, Fund. Math. 14 (1929) 132-137.
• [5] W. Kulpa, Poincaré and domain invariance theorem, Acta Univ. Carolinae - Mathematica et Physica 39 (1998) 127-136.
• [6] G. van der Laan, D. Talman and Z. Yang, Intersection theorems on polytypes, Math. Programming 84 (1999) 333-352.
• [7] G. van der Laan, D. Talman and Z. Yang, Existence of balanced simplices on polytopes, J. Combin. Theory (A) 96 (2001) 25-38, doi: 10.1006/jcta.2001.3178.
• [8] L.S. Shapley, On balanced games without side payments, in: T.C. Hu and S.M. Robinson (eds.), Mathematical Programming (New York: Academic Press, 1973) 261-290.
• [9] E. Sperner, Neuer beweis für die invarianz der dimensionszahl und des gebiets, Abh. Math. Sem. Univ. Hamburg 6 (1928) 265-272, doi: 10.1007/BF02940617.

Identyfikatory

DOI

10.7151/dmgt.1264