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2010 MULTIPLE COMBINATORIAL STOKES’ THEOREM WITH BALANCED STRUCTURE
Shyh-Nan Lee, Chien-Hung Chen, Mau-Hsiang Shih
Taiwanese J. Math. 14(3B): 1169-1200 (2010). DOI: 10.11650/twjm/1500405912

Abstract

Combinatorics of complexes plays an important role in topology, nonlinear analysis, game theory, and mathematical economics. In 1967, Ky Fan used door-to-door principle to prove a combinatorial Stokes’ theorem on pseudomanifolds. In 1993, Shih and Lee developed the geometric context of general position maps, $\pi$-balanced and $\pi$-subbalanced sets and used them to prove a combinatorial formula for multiple set-valued labellings on simplexes. On the other hand, in 1998, Lee and Shih proved a multiple combinatorial Stokes’ theorem, generalizing the Ky Fan combinatorial formula to multiple labellings. That raises a question : Does there exist a unified theorem underlying Ky Fan’s theorem and Shih and Lee’s results? In this paper, we prove a multiple combinatorial Stokes’ theorem with balanced structure. Our method of proof is based on an incidence function. As a consequence, we obtain a multiple combinatorial Sperner’s lemma with balanced structure.

Citation

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Shyh-Nan Lee. Chien-Hung Chen. Mau-Hsiang Shih. "MULTIPLE COMBINATORIAL STOKES’ THEOREM WITH BALANCED STRUCTURE." Taiwanese J. Math. 14 (3B) 1169 - 1200, 2010. https://doi.org/10.11650/twjm/1500405912

Information

Published: 2010
First available in Project Euclid: 18 July 2017

zbMATH: 1209.05019
MathSciNet: MR2674603
Digital Object Identifier: 10.11650/twjm/1500405912

Subjects:
Primary: 05A19, 47H10, 52B05

Rights: Copyright © 2010 The Mathematical Society of the Republic of China

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Vol.14 • No. 3B • 2010
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