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A Journey Through Discrete MathematicsUsing Brouwer’s Fixed Point Theorem

A Journey Through Discrete Mathematics: Using Brouwer’s Fixed Point Theorem [Brouwer’s fixed point theorem from 1911 is a basic result in topology—with a wealth of combinatorial and geometric consequences. In these lecture notes we present some of them, related to the game of HEX and to the piercing of multiple intervals. We also sketch stronger theorems, due to Oliver and others, and explain their applications to the fascinating (and still not fully solved) evasiveness problem.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Journey Through Discrete MathematicsUsing Brouwer’s Fixed Point Theorem

Editors: Loebl, Martin; Nešetřil, Jaroslav; Thomas, Robin
Björner, Anders; Matoušek, Jiří; Ziegler, Günter M.
Springer Journals — May 9, 2017
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Publisher
Springer International Publishing
Copyright
© Springer International publishing AG 2017
ISBN
978-3-319-44478-9
Pages
221 –271
DOI
10.1007/978-3-319-44479-6_10
Publisher site
See Chapter on Publisher Site

Abstract

[Brouwer’s fixed point theorem from 1911 is a basic result in topology—with a wealth of combinatorial and geometric consequences. In these lecture notes we present some of them, related to the game of HEX and to the piercing of multiple intervals. We also sketch stronger theorems, due to Oliver and others, and explain their applications to the fascinating (and still not fully solved) evasiveness problem.]

Published: May 9, 2017

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