Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 8, Tome 231 (1995), pp. 245-254
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Boris M. Bekker; Nikita Yu. Netsvetaev. Generalized Sperner lemma and subdivisions into simplices of equal volume. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 8, Tome 231 (1995), pp. 245-254. http://geodesic.mathdoc.fr/item/ZNSL_1995_231_a16/
@article{ZNSL_1995_231_a16,
author = {Boris M. Bekker and Nikita Yu. Netsvetaev},
title = {Generalized {Sperner} lemma and subdivisions into simplices of equal volume},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {245--254},
year = {1995},
volume = {231},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_231_a16/}
}
TY - JOUR
AU - Boris M. Bekker
AU - Nikita Yu. Netsvetaev
TI - Generalized Sperner lemma and subdivisions into simplices of equal volume
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1995
SP - 245
EP - 254
VL - 231
UR - http://geodesic.mathdoc.fr/item/ZNSL_1995_231_a16/
LA - en
ID - ZNSL_1995_231_a16
ER -
%0 Journal Article
%A Boris M. Bekker
%A Nikita Yu. Netsvetaev
%T Generalized Sperner lemma and subdivisions into simplices of equal volume
%J Zapiski Nauchnykh Seminarov POMI
%D 1995
%P 245-254
%V 231
%U http://geodesic.mathdoc.fr/item/ZNSL_1995_231_a16/
%G en
%F ZNSL_1995_231_a16
A generalization of the well-known Sperner lemma is suggested, which covers the case of arbitrary subdivisions of (convex) polyhedra into (convex) polyhedra. It is used for giving a new proof of the Thomas–Monsky–Mead theorem saying that the $n$-cube can be subdivided into $N$ simplices of equal volume if and only if $N$ is divisible by $n!$. Some new related results are announced. Bibl. 6 titles.
