A constructive proof of a permutation-based generalization of Sperner's lemma

DOI10.1007/BF01587081zbMath0673.55004WikidataQ56286472 ScholiaQ56286472MaRDI QIDQ1120843

Ravindra B. Bapat

Publication date: 1989

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

zbMATH Keywords

Brouwer's fixed point theoremSperner's lemmaKKM lemmasimplicial paths in a triangulationsimplicial pivoting

Mathematics Subject Classification ID

Fixed points and coincidences in algebraic topology (55M20) Graph theory (05C99) Dimension theory in algebraic topology (55M10) Designs and configurations (05B99) PL-topology (57Q99) Classical topics in algebraic topology (55M99)

Related Items (14)

KKM type theorems with boundary conditions ⋮ ENVY‐FREE DIVISION USING MAPPING DEGREE ⋮ Fair Division and Generalizations of Sperner- and KKM-type Results ⋮ Combinatorial Stokes formulae ⋮ Equivalent forms of the Brouwer fixed point theorem. II. ⋮ A direct proof of Shapley-Sperner's lemma based on the KKMS lemma ⋮ Combinatorial integer labeling theorems on finite sets with applications ⋮ EQUILIBRIUM IN A DISCRETE EXCHANGE ECONOMY WITH REGIONAL SUB-ECONOMIES ⋮ Unnamed Item ⋮ Existence of balanced simplices on polytopes. ⋮ Democratic fair allocation of indivisible goods ⋮ Multilabeled Versions of Sperner's and Fan's Lemmas and Applications ⋮ Almost envy-free allocations with connected bundles ⋮ Combinatorial formulae for multiple set-valued labellings

Cites Work

• Unnamed Item
• Equilibrium in a discrete exchange economy with money
• The computation of fixed points and applications
• Variable Dimension Complexes Part II: A Unified Approach to Some Combinatorial Lemmas in Topology
• Combinatorial Theorems on the Simplotope that Generalize Results on the Simplex and Cube
• Orientation in Complementary Pivot Algorithms
• On generalizing shapley's index theory to labelled pseudomanifolds
• Equilibrium Points of Bimatrix Games
• Simplicial maps from an orientable n-pseudomanifold into Sm with the octahedral triangulation
• The Approximation of Fixed Points of a Continuous Mapping
• On the Sperner lemma

This page was built for publication: A constructive proof of a permutation-based generalization of Sperner's lemma