Multilabeled Versions of Sperner's and Fan's Lemmas and Applications

DOI10.1137/18M1192548zbMath1427.55002arXiv1801.02044WikidataQ124846300 ScholiaQ124846300MaRDI QIDQ5234532

Frédéric Meunier, Francis Edward Su

Publication date: 27 September 2019

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.02044

zbMATH Keywords

graph coloringSperner's lemmacake-cuttinglabelingsFan's lemmaconsensus-halving

Mathematics Subject Classification ID

Fixed-point and coincidence theorems (topological aspects) (54H25) Fixed points and coincidences in algebraic topology (55M20) Resource and cost allocation (including fair division, apportionment, etc.) (91B32) Combinatorial aspects of simplicial complexes (05E45)

Related Items (6)

Fair distributions for more participants than allocations ⋮ Envy-free division of multi-layered cakes ⋮ Generalized Rental Harmony ⋮ How to Cut a Cake Fairly: A Generalization to Groups ⋮ Discrete geometry. Abstracts from the workshop held September 20--26, 2020 (hybrid meeting) ⋮ Envy-free division in the presence of a dragon

Cites Work

• Unnamed Item
• Colorful subhypergraphs in uniform hypergraphs
• Kneser's conjecture, chromatic number, and homotopy
• Equilibrium in a discrete exchange economy with money
• Local chromatic number, Ky Fan's theorem, and circular colorings
• Necklace bisection with one cut less than needed
• Splitting necklaces
• A constructive proof of a permutation-based generalization of Sperner's lemma
• Dividing a cake fairly
• A counting lemma and multiple combinatorial Stokes' theorem
• Consensus-halving via theorems of Borsuk-Ulam and Tucker
• A polytopal generalization of Sperner's lemma
• Oriented matroids and Ky Fan's theorem
• Colourful theorems and indices of homomorphism complexes
• Strengthening topological colorful results for graphs
• Combinatorial necklace splitting
• Splitting multidimensional necklaces
• A constructive proof of Ky Fan's generalization of Tucker's lemma
• A generalization of Tucker's combinatorial lemma with topological applications
• Rental Harmony: Sperner's Lemma in Fair Division
• A Borsuk–Ulam Equivalent that Directly Implies Sperner’s Lemma
• Bisection of Circle Colorings
• STRENGTHENING OF SPERNER'S LEMMA APPLIED TO HOMOLOGY THEORY
• How to Cut a Cake Fairly
• Fair Division and Generalizations of Sperner- and KKM-type Results
• Achieving Rental Harmony with a Secretive Roommate
• The Borsuk-Ulam Theorem and Bisection of Necklaces
• A Moment Problem in L 1 Approximation
• Equivalent Formulations of the Borsuk-Ulam Theorem

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