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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Dissection of the hypercube into simplexes


Author: D. G. Mead
Journal: Proc. Amer. Math. Soc. 76 (1979), 302-304
MSC: Primary 52A25
MathSciNet review: 537093
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Abstract: A generalization of Sperner's Lemma is proved and, using extensions of p-adic valuations to the real numbers, it is shown that the unit hypercube in n dimensions can be divided into m simplexes all of equal hypervolume if and only if m is a multiple of n!. This extends the corresponding result for $ n = 2$ of Paul Monsky.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0537093-6
Keywords: Sperner's Lemma, p-adic valuation, dissection of a unit hypercube into simplexes
Article copyright: © Copyright 1979 American Mathematical Society