A polytopal generalization of Sperner's lemma

DOI10.1006/jcta.2002.3274zbMath1015.05089OpenAlexW2101942472WikidataQ56286471 ScholiaQ56286471MaRDI QIDQ1865380

Francis Edward Su, Elisha Peterson, Jesús A. De Loera

Publication date: 26 March 2003

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1680&context=hmc_fac_pub

zbMATH Keywords

Sperner's lemmapebble setssimplicial covers of polytopestriangulations of polytopes

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Extremal set theory (05D05)

Related Items (19)

Sperner labellings: A combinatorial approach ⋮ KKM type theorems with boundary conditions ⋮ Fair division with multiple pieces ⋮ Combinatorial approach to detection of fixed points, periodic orbits, and symbolic dynamics ⋮ Sperner’s Colorings and Optimal Partitioning of the Simplex ⋮ Fair Division and Generalizations of Sperner- and KKM-type Results ⋮ Using volume to prove Sperner's Lemma ⋮ Envy-free two-player \(m\)-cake and three-player two-cake divisions ⋮ Pebble sets in convex polygons ⋮ A simplicial homology algorithm for Lipschitz optimisation ⋮ Extensions of Sperner and Tucker's lemma for manifolds ⋮ Different versions of the nerve theorem and colourful simplices ⋮ Two-player envy-free multi-cake division ⋮ Alternate Heegaard genus bounds distance ⋮ Wait-free approximate agreement on graphs ⋮ Wait-free approximate agreement on graphs ⋮ Multilabeled Versions of Sperner's and Fan's Lemmas and Applications ⋮ The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg ⋮ A constructive proof of Ky Fan's generalization of Tucker's lemma

Cites Work

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• Lectures on Polytopes
• The Approximation of Fixed Points of a Continuous Mapping
• On the Sperner lemma
• SIMPLICIAL APPROXIMATION OF FIXED POINTS

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